Unit 6 Practice Quiz Basic Geometry

1. Find the perimeter of a square in which the sides are equal to 13.5 cm.

54 cm

24 cm

182.25 cm

91.125 cm

The perimeter of a square is calculated by multiplying the length of one side by 4. In this case, since the sides of the square are equal to 13.5 cm, the perimeter would be 4 times 13.5 cm, which equals 54 cm.

Explanation

The perimeter of a square is calculated by multiplying the length of one side by 4. In this case, since the sides of the square are equal to 13.5 cm, the perimeter would be 4 times 13.5 cm, which equals 54 cm.

2. A triangle has a 110' angle and a 35' angle. Find the measure of the third angle.
(Note: ' stands for degree)

215'

35'

75'

45'

The sum of the angles in a triangle is always 180 degrees. Therefore, to find the measure of the third angle, we can subtract the measures of the given angles (110' and 35') from 180 degrees. The remaining angle would be the measure of the third angle. In this case, 180 - 110 - 35 = 35 degrees.

Explanation

The sum of the angles in a triangle is always 180 degrees. Therefore, to find the measure of the third angle, we can subtract the measures of the given angles (110' and 35') from 180 degrees. The remaining angle would be the measure of the third angle. In this case, 180 - 110 - 35 = 35 degrees.

3. Find the complement of a 54' angle.
(Note: ' stands for degree)

306'

126'

36'

46'

The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. In this case, the given angle is 54 degrees. To find the complement, we subtract the given angle from 90 degrees. Therefore, the complement of a 54' angle is 36'.

Explanation

The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. In this case, the given angle is 54 degrees. To find the complement, we subtract the given angle from 90 degrees. Therefore, the complement of a 54' angle is 36'.

4. A metal frame is being built to install around a rectangular sign that is 2 m wide and 3.5 m long. At $4.24 per meter, find the cost of the material for the frame.

$31.36

$14.84

$23.32

$46.64

To find the cost of the material for the frame, we need to calculate the perimeter of the rectangular sign. The perimeter is equal to twice the sum of the width and length. Therefore, the perimeter is 2(2+3.5) = 2(5.5) = 11 m.

Since the cost is given as $4.24 per meter, we can multiply the perimeter by the cost per meter to find the total cost.

11 m * $4.24/m = $46.64

Therefore, the cost of the material for the frame is $46.64.

Explanation

To find the cost of the material for the frame, we need to calculate the perimeter of the rectangular sign. The perimeter is equal to twice the sum of the width and length. Therefore, the perimeter is 2(2+3.5) = 2(5.5) = 11 m.

Since the cost is given as $4.24 per meter, we can multiply the perimeter by the cost per meter to find the total cost.

11 m * $4.24/m = $46.64

Therefore, the cost of the material for the frame is $46.64.

5. Find the area of a triangle with a base of 10 ft and a height of 16 ft.

(Note: ft^2 means ft squared)

160 ft^2

26 ft^2

80 ft^2

320 ft^2

To find the area of a triangle, you can use the formula A = (1/2) * base * height. In this case, the base is 10 ft and the height is 16 ft. Plugging these values into the formula, we get A = (1/2) * 10 ft * 16 ft = 80 ft^2. Therefore, the correct answer is 80 ft^2.

Explanation

To find the area of a triangle, you can use the formula A = (1/2) * base * height. In this case, the base is 10 ft and the height is 16 ft. Plugging these values into the formula, we get A = (1/2) * 10 ft * 16 ft = 80 ft^2. Therefore, the correct answer is 80 ft^2.

6. A silo, which is in the shape of a cylinder, is 24 ft in diameter and has a height of 40 ft. Find the volume of the silo.
(Note: ft^3 means ft cubed)

3014.4 ft^3

1507.2 ft^3

18086.4 ft^3

5760 ft^3

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, the diameter is given as 24 ft, so the radius is half of that, which is 12 ft. The height is given as 40 ft. Plugging these values into the formula, we get V = π(12^2)(40) = 18086.4 ft^3. Therefore, the correct answer is 18086.4 ft^3.

Explanation

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. In this case, the diameter is given as 24 ft, so the radius is half of that, which is 12 ft. The height is given as 40 ft. Plugging these values into the formula, we get V = π(12^2)(40) = 18086.4 ft^3. Therefore, the correct answer is 18086.4 ft^3.

7. Find the volume of a sphere with a 5-foot diameter.
(Note: ft^3 means ft cubed)

65.42 ft^3

62.80 ft^3

26.17 ft^3

78.50 ft^3

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, the diameter of the sphere is given as 5 feet, so the radius would be half of that, which is 2.5 feet. Plugging this value into the formula, we get V = (4/3)π(2.5)^3 = 65.42 ft^3. Therefore, the correct answer is 65.42 ft^3.

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, the diameter of the sphere is given as 5 feet, so the radius would be half of that, which is 2.5 feet. Plugging this value into the formula, we get V = (4/3)π(2.5)^3 = 65.42 ft^3. Therefore, the correct answer is 65.42 ft^3.