Area Of Shapes Quiz And Volume.

1. Let's say that a garden has a width of 4 and a length of 6 what's the area?

26

24

24.1

29

The area of a rectangle can be calculated by multiplying its length and width. In this case, the width is given as 4 and the length is given as 6. Multiplying these two values, we get 4 * 6 = 24. Therefore, the area of the garden is 24.

Explanation

The area of a rectangle can be calculated by multiplying its length and width. In this case, the width is given as 4 and the length is given as 6. Multiplying these two values, we get 4 * 6 = 24. Therefore, the area of the garden is 24.

2. To get the volume of a cylinder, you have to use the formula( base to the second power times height.)

True

False

The explanation for the given correct answer is that to calculate the volume of a cylinder, you need to use the formula of the base area (which is the base to the second power) multiplied by the height of the cylinder. This formula is derived from the geometric properties of a cylinder and is widely accepted and used in mathematics and engineering. Therefore, the statement "To get the volume of a cylinder, you have to use the formula (base to the second power times height)" is true.

Explanation

The explanation for the given correct answer is that to calculate the volume of a cylinder, you need to use the formula of the base area (which is the base to the second power) multiplied by the height of the cylinder. This formula is derived from the geometric properties of a cylinder and is widely accepted and used in mathematics and engineering. Therefore, the statement "To get the volume of a cylinder, you have to use the formula (base to the second power times height)" is true.

3. Let's say that kylo and kraig both have a trapezoid shaped hat, that's green and yellow, and both have a base of 6 the top and a base of seven, and finally a height of 3, what's the area of the trapezoid?

30

19.5cm2

15cm2

15cm3

The area of a trapezoid can be calculated using the formula: (base1 + base2) * height / 2. In this case, the base1 is 6, the base2 is 7, and the height is 3. Plugging these values into the formula, we get (6 + 7) * 3 / 2 = 13 * 3 / 2 = 39 / 2 = 19.5. Therefore, the area of the trapezoid is 19.5 cm2.

Explanation

The area of a trapezoid can be calculated using the formula: (base1 + base2) * height / 2. In this case, the base1 is 6, the base2 is 7, and the height is 3. Plugging these values into the formula, we get (6 + 7) * 3 / 2 = 13 * 3 / 2 = 39 / 2 = 19.5. Therefore, the area of the trapezoid is 19.5 cm2.

4. The volume of a triangle with the dimensions of 6, 7, and 10 has a volume of 210.

True

False

A triangle is a two-dimensional figure and does not have volume. Volume is a measure of the amount of space a three-dimensional object occupies, while a triangle only has area, which is the amount of space it covers on a flat surface. The formula used to calculate the area of a triangle is ½ * base * height. Therefore, a triangle with dimensions 6, 7, and 10 cannot have a volume of 210.

Explanation

A triangle is a two-dimensional figure and does not have volume. Volume is a measure of the amount of space a three-dimensional object occupies, while a triangle only has area, which is the amount of space it covers on a flat surface. The formula used to calculate the area of a triangle is ½ * base * height. Therefore, a triangle with dimensions 6, 7, and 10 cannot have a volume of 210.

5. If mike has a parallelogram shaped table, and it has these dimensions of the parallelogram shown here what's the area of it?

28 cm^2

29 cm^2

25 cm^2

46 cm^2

The area of a parallelogram is calculated by multiplying the base by the height. In this case, the base is 7 and the height is 4. Therefore, the area of the parallelogram is 7 * 4 = 28.

Explanation

The area of a parallelogram is calculated by multiplying the base by the height. In this case, the base is 7 and the height is 4. Therefore, the area of the parallelogram is 7 * 4 = 28.

6. A circle has a diameter of 5, what's the circumference?

16.75

15.70

12.35

19.35

The circumference of a circle can be calculated using the formula C = πd, where d is the diameter. In this case, the diameter is given as 5. Plugging this value into the formula, we get C = π * 5 = 15.70. Therefore, the correct answer is 15.70.

Explanation

The circumference of a circle can be calculated using the formula C = πd, where d is the diameter. In this case, the diameter is given as 5. Plugging this value into the formula, we get C = π * 5 = 15.70. Therefore, the correct answer is 15.70.

7. Which of the following statements about the volume of a triangular prism is correct?

A triangle with dimensions 6, 7, and 10 has a volume of 210.

Triangles are three-dimensional shapes with a calculable volume.

The volume of a triangular prism is calculated by multiplying the area of the triangular base by the height of the prism.

The volume of a triangle is always half the product of its base and height.

A triangle itself is a two-dimensional figure and does not have volume. However, a triangular prism, a three-dimensional object with two triangular bases and three rectangular sides, does have a volume. This volume is determined by multiplying the area of one of the triangular bases by the height (or length) of the prism.

Explanation

A triangle itself is a two-dimensional figure and does not have volume. However, a triangular prism, a three-dimensional object with two triangular bases and three rectangular sides, does have a volume. This volume is determined by multiplying the area of one of the triangular bases by the height (or length) of the prism.

8. Carlos is making a tower, the base is 7 by 6, he is planning to have a height of 8, what's the full volume when it is finished?

336

334

336.1

336cm2

The volume of a rectangular prism can be calculated by multiplying the length, width, and height. In this case, the base of the tower is 7 by 6, so the area of the base is 7 * 6 = 42 square units. The height of the tower is 8 units. Therefore, the volume of the tower is 42 * 8 = 336 cubic units.

Explanation

The volume of a rectangular prism can be calculated by multiplying the length, width, and height. In this case, the base of the tower is 7 by 6, so the area of the base is 7 * 6 = 42 square units. The height of the tower is 8 units. Therefore, the volume of the tower is 42 * 8 = 336 cubic units.

9. Kalb and his friend damian, have a striped ball. The balls' full measure is 3500, with dimensions of 50 and and 35, what's the depth?

2

3

2.5

2cm2

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Explanation

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10. Jerry has a rhombus shaped kite, the dimensions are 6 and 7, then Jerry's mom stiches, both 2cm more, what's the area of his kite?

21

36

35.5

22

After Jerry's mom stitches the kite, the dimensions become 8 and 9 (6+2 and 7+2). The area of a rhombus is calculated by multiplying the lengths of its diagonals and dividing by 2. In this case, the diagonals are 8 and 9. So, the area of the kite is (8 * 9) / 2 = 36.

Explanation

After Jerry's mom stitches the kite, the dimensions become 8 and 9 (6+2 and 7+2). The area of a rhombus is calculated by multiplying the lengths of its diagonals and dividing by 2. In this case, the diagonals are 8 and 9. So, the area of the kite is (8 * 9) / 2 = 36.

11. If Sarah has two cones, which has a base of 3 and height of 6, she wants to find the volume, what is the volume of both the cones?( don't forget to put PI.)

36.5

36PI

54/3PI

18PI

The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height. In this case, the base of the cones has a radius of 3 and a height of 6. Plugging these values into the formula, we get V = (1/3) * π * 3^2 * 6 = 36π. Therefore, the correct answer is 36π.

Explanation

The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height. In this case, the base of the cones has a radius of 3 and a height of 6. Plugging these values into the formula, we get V = (1/3) * π * 3^2 * 6 = 36π. Therefore, the correct answer is 36π.

12. Tim has 3 poles, one has a base of 3 and height of 5, the other then has a base of 6 and height of 7, the final one has a base of 4 and height of ten. What's the sum of all the volume in each cone?

457

458

92

397

The question asks for the sum of the volumes of each cone. To find the volume of a cone, we use the formula V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.

For the first cone, the base has a radius of 3/2 and a height of 5. So the volume of the first cone is (1/3) * π * (3/2)^2 * 5.

For the second cone, the base has a radius of 6/2 and a height of 7. So the volume of the second cone is (1/3) * π * (6/2)^2 * 7.

For the third cone, the base has a radius of 4/2 and a height of 10. So the volume of the third cone is (1/3) * π * (4/2)^2 * 10.

Adding up the volumes of the three cones gives us the sum of the volumes, which is approximately 457.

Explanation

The question asks for the sum of the volumes of each cone. To find the volume of a cone, we use the formula V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.

For the first cone, the base has a radius of 3/2 and a height of 5. So the volume of the first cone is (1/3) * π * (3/2)^2 * 5.

For the second cone, the base has a radius of 6/2 and a height of 7. So the volume of the second cone is (1/3) * π * (6/2)^2 * 7.

For the third cone, the base has a radius of 4/2 and a height of 10. So the volume of the third cone is (1/3) * π * (4/2)^2 * 10.

Adding up the volumes of the three cones gives us the sum of the volumes, which is approximately 457.

13. What's the formula of calculating the volume of a sphere?

4 divide by three times rPI

Four divided by three pi R

4/3 times r to the third power

PiR times 4/3

The formula for calculating the volume of a sphere is 4/3 times r to the third power.

Explanation

The formula for calculating the volume of a sphere is 4/3 times r to the third power.

14. Look at the circle with a cut part into a fraction chose which one is the full formula of it.

8 to the second power=64 then 64/4=16

4 to the second power=16 then 3/4 times 16PI=48/4=12PI

8 to the second power=64 then 3/4 times 64=192/4=48PI

2 to the second power=4 then 3/4 times 4 PI=12/4=3PI

The correct answer is the option that correctly calculates the area of the circle with a cut part into a fraction. The formula for the area of a circle is πr^2, where r is the radius. The given answer correctly calculates the area by squaring 4 (the radius) to get 16, then multiplying it by 3/4 and π to get 12π.

Explanation

The correct answer is the option that correctly calculates the area of the circle with a cut part into a fraction. The formula for the area of a circle is πr^2, where r is the radius. The given answer correctly calculates the area by squaring 4 (the radius) to get 16, then multiplying it by 3/4 and π to get 12π.

15. Mylo has a sphere shaped chair, he figured that the diameter is 14, what is the volume of his chair? Round if need to.

1437( from decimal

1439(from decimal

1437PI(from decimal

1436PI(from decimal

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, we are given the diameter, which is 14. The radius can be found by dividing the diameter by 2, so the radius is 14/2 = 7. Plugging this value into the formula, we get V = (4/3)π(7^3) = (4/3)π(343) = 1437π (rounded if necessary). Therefore, the volume of mylo's chair is 1437π.

Explanation

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. In this case, we are given the diameter, which is 14. The radius can be found by dividing the diameter by 2, so the radius is 14/2 = 7. Plugging this value into the formula, we get V = (4/3)π(7^3) = (4/3)π(343) = 1437π (rounded if necessary). Therefore, the volume of mylo's chair is 1437π.

16. If Anna has a triangular shaped cake, and she wants to find the area, with a height of 4 and base of 4 what's the area?

16

8.5

19

8

To find the area of a triangular cake, you can use the formula for the area of a triangle which is 1/2 * base * height. In this case, the base is given as 4 and the height is also given as 4. Plugging these values into the formula, we get 1/2 * 4 * 4 = 8. Therefore, the area of the triangular cake is 8.

Explanation

To find the area of a triangular cake, you can use the formula for the area of a triangle which is 1/2 * base * height. In this case, the base is given as 4 and the height is also given as 4. Plugging these values into the formula, we get 1/2 * 4 * 4 = 8. Therefore, the area of the triangular cake is 8.

17. Mary and alete have an aqariuam. The water is 3.5 cm high. 4.7 cm deep, and finally it's a circle shape. If the volume is 16.45, and the radius is 4, what's the volume?

251.55

251.55PI

234.57

257.89PI

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Explanation

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18. A pool has, a full measure of 3625, the dimensions are the following, 25 and 35, what's the depth of the pool?

4

5

3.5

3

The volume of a rectangular pool is calculated by multiplying its length, width, and depth. In this case, the volume is 3625, the length is 25, and the width is 35. To find the depth, we can rearrange the formula:

Depth = Volume / (Length * Width)

Depth = 3625 / (25 * 35) = 4.14

The closest answer to this is 4.

Explanation

The volume of a rectangular pool is calculated by multiplying its length, width, and depth. In this case, the volume is 3625, the length is 25, and the width is 35. To find the depth, we can rearrange the formula:

Depth = Volume / (Length * Width)

Depth = 3625 / (25 * 35) = 4.14

The closest answer to this is 4.

19. Let's say that jane and her brother jack, is playing a game, it' called prime area, the goal is to get three cards and see if it has any prime numbers that can multiply into the area of a circle or sphere On the third turn jane got 7,4 and 5, and the total was in decimals, which are the possible combonations jane can use?

Circle area=120.98

Sphere volume=523.6

Circle area=78.5

Sphere volume=1436.8

not-available-via-ai

Explanation

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Submit

20. The volume of the cuboid in the image is

To find the volume of a cuboid, you multiply together the lengths of its three dimensions: length, width, and height.

Given that the sides of the cuboid are 3, 3, and 2:

Volume = length × width × height

Volume = 3 × 3 × 2

Volume = 18 cubic units

So, the volume of the cuboid is 18 cubic units.

Explanation

To find the volume of a cuboid, you multiply together the lengths of its three dimensions: length, width, and height.

Given that the sides of the cuboid are 3, 3, and 2:

Volume = length × width × height

Volume = 3 × 3 × 2

Volume = 18 cubic units

So, the volume of the cuboid is 18 cubic units.

Submit

21. Look at this bench on the side, what is the area of it, without the benches?( please note the traingles height is 3.3 and base is 3.3, nine is the full legnth.)

91.81

70.19

37.44

38.44

The area of the bench without the benches can be calculated by finding the area of the entire bench and subtracting the area of the benches. Since the height and base of the triangle are both 3.3, the area of the triangle is (1/2) * 3.3 * 3.3 = 5.445. The area of the rectangle is 3.3 * 9 = 29.7. Therefore, the area of the entire bench is 5.445 + 29.7 = 35.145. Since the area of the benches is not given, we cannot subtract it from the total area. Therefore, the correct answer cannot be determined from the given information.

Explanation

The area of the bench without the benches can be calculated by finding the area of the entire bench and subtracting the area of the benches. Since the height and base of the triangle are both 3.3, the area of the triangle is (1/2) * 3.3 * 3.3 = 5.445. The area of the rectangle is 3.3 * 9 = 29.7. Therefore, the area of the entire bench is 5.445 + 29.7 = 35.145. Since the area of the benches is not given, we cannot subtract it from the total area. Therefore, the correct answer cannot be determined from the given information.

22. Bob and tammy made two different shapes, a circle and triangle, the circumference of tammy's circle is 200.96, the triangle has a height of 35, the area is 8.749 to the nearest hundredths, what is the area of the circle and the height of the triangle.

Height=25 and area=1024

Height=25 and area=1156PI

Height=25 area=5678

Height=25 and area=3215.36PI

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Explanation

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23. A cube has dimensions of 3/4, 2 and finally 6, how many 1/4' can fit inside?

576/4

36

576

548

The given cube has dimensions of 3/4, 2, and 6. To find out how many 1/4' cubes can fit inside, we need to calculate the volume of the larger cube and divide it by the volume of the smaller cube. The volume of the larger cube is (3/4) * 2 * 6 = 9/4. The volume of the smaller cube is (1/4) * (1/4) * (1/4) = 1/64. Dividing the volume of the larger cube by the volume of the smaller cube gives us (9/4) / (1/64) = 576. Therefore, 576 1/4' cubes can fit inside the given cube.

Explanation

The given cube has dimensions of 3/4, 2, and 6. To find out how many 1/4' cubes can fit inside, we need to calculate the volume of the larger cube and divide it by the volume of the smaller cube. The volume of the larger cube is (3/4) * 2 * 6 = 9/4. The volume of the smaller cube is (1/4) * (1/4) * (1/4) = 1/64. Dividing the volume of the larger cube by the volume of the smaller cube gives us (9/4) / (1/64) = 576. Therefore, 576 1/4' cubes can fit inside the given cube.

24. Match the following

circle with radius=5

6.7 cup with water, then tom put's a ring in a 7.3 cup, with bases of 4 and five what's the volume of his ring?

a rhombus with lengths with 7 and 8 has a area of.

3455 in all, 95 and 11 depth=

Submit

25. John has a cup of water which measures 8.9, then the cup with a ring measures 9.2, and the bottom bases are 5 and 2, what's the volume of john's ring?

1.5

6.8

3

0.3

The volume of the cup can be calculated by subtracting the volume of the bottom base (5) from the volume of the cup with the ring (9.2). So, the volume of the cup is 9.2 - 5 = 4.2. Since the volume of the cup is 8.9, the volume of the ring can be calculated by subtracting the volume of the cup (8.9) from the volume of the cup with the ring (9.2). So, the volume of the ring is 9.2 - 8.9 = 0.3. Therefore, the volume of John's ring is 0.3.

Explanation

The volume of the cup can be calculated by subtracting the volume of the bottom base (5) from the volume of the cup with the ring (9.2). So, the volume of the cup is 9.2 - 5 = 4.2. Since the volume of the cup is 8.9, the volume of the ring can be calculated by subtracting the volume of the cup (8.9) from the volume of the cup with the ring (9.2). So, the volume of the ring is 9.2 - 8.9 = 0.3. Therefore, the volume of John's ring is 0.3.