1.
A cylindrical container has a diameter of 12 inches and a height of 15 inches. What is the volume of this container to the nearest tenth of a cubic inch?
Correct Answer
C. 1696.5 in^{3}
Explanation
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height. In this case, the diameter is given as 12 inches, so the radius would be half of that, which is 6 inches. Plugging in the values, V = π(6^2)(15) = 1696.5 in3. Therefore, the correct answer is 1696.5 in3.
2.
A right cone has a height of 6 feet and a volume of 32π cubic feet. What is its radius?
Correct Answer
D. 4 ft
Explanation
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. In this case, we are given the height (6 ft) and the volume (32π cubic feet). Plugging these values into the formula, we can solve for the radius. By rearranging the formula, we get r^2 = (3V)/(πh), and substituting the given values, we find r^2 = (3*32π)/(π*6) = 16. Taking the square root of both sides, we find that the radius is 4 ft.
3.
Find the surface area!
Correct Answer
A. 556 cm^{2}
4.
Find the height of a cylinder if the surface area is 198.8 mm^{2 } and the radius is 2.8 mm
Correct Answer
A. 11.3mm
Explanation
The height of a cylinder can be found using the formula for the surface area of a cylinder, which is 2πrh + 2πr^2, where r is the radius and h is the height. In this case, the surface area is given as 198.8 mm^2 and the radius is 2.8 mm. By substituting these values into the formula and solving for h, we find that the height is 11.3 mm.
5.
What is the volume of a cylinder if the radius is 8 ft and the height is 5 ft (round to the nearest tenth)
Correct Answer
D. 1005.3 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. Plugging in the given values, we get V = π(8^2)(5) = π(64)(5) = 320π ft^3. Rounding to the nearest tenth, we get approximately 1005.3 ft^3.
6.
What is the surface area of this triangular prism?
Correct Answer
A. 110 in^{2}
7.
Find the volume of the triangular prism.
Correct Answer
D. 40 cm³
8.
Lucia has a triangular prism that has a length of 6cm and the width of 4cm and the height is 8cm. What is the volume
Correct Answer
A. 96cm³
Explanation
The volume of a triangular prism can be calculated by multiplying the base area (which is the area of the triangular base) by the height. In this case, the triangular base has a length of 6cm and a width of 4cm, so its area is (1/2) * 6cm * 4cm = 12cm². Multiplying this by the height of 8cm gives a volume of 96cm³.
9.
Campbell Soup is creating a new soup label. If a can has a height of 12 cm and a diameter of 6 cm, how much material does Campbell need for each soup label? Use 3.14 for π.
Correct Answer
D. 75.36 in^{2}
Explanation
The question asks for the amount of material needed for each soup label. To find this, we need to calculate the surface area of the can. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. Given that the diameter is 6 cm, the radius is 3 cm. Plugging in these values, we get 2 * 3.14 * 3^2 + 2 * 3.14 * 3 * 12 = 150.72 cm^2. However, the answer options are in square inches, so we need to convert cm^2 to in^2. Since 1 cm^2 is approximately equal to 0.155 in^2, 150.72 cm^2 is approximately equal to 23.36 in^2. Therefore, the correct answer is 75.36 in^2.
10.
Jesse needs to wrap the present shown below. How much wrapping paper would he need?
Correct Answer
C. 327 in^{2}
Explanation
Jesse would need 327 in2 of wrapping paper to wrap the present shown below.
11.
The capacity of a rectangular tank is 189 kiloliters. it is 7 m long and 4.5 m high. Find its breadth.
Correct Answer
A. 6 m
Explanation
The capacity of a rectangular tank is determined by multiplying its length, breadth, and height. In this case, we are given the length (7 m) and height (4.5 m), and the capacity (189 kiloliters). To find the breadth, we can rearrange the formula for capacity and solve for breadth. Dividing the capacity by the product of length and height, we get 189 kiloliters / (7 m * 4.5 m) = 6 m. Therefore, the breadth of the tank is 6 m.
12.
If the diameter of right circular cylinder is 18cm with the height of 28cm and value of pi = 3.142 then the total surface area of the cylinder is
Correct Answer
A. 2092.572cm²
Explanation
The formula to calculate the total surface area of a right circular cylinder is 2πr(r+h), where r is the radius and h is the height of the cylinder. In this case, the diameter is given as 18cm, so the radius would be half of that, which is 9cm. Plugging in the values, we get 2 * 3.142 * 9(9+28) = 2 * 3.142 * 9 * 37 = 2092.572cm². Therefore, the correct answer is 2092.572cm².
13.
Find the volume of a cube of side 8 cm.
Correct Answer
B. 512 cm^{3}
Explanation
The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the side of the cube is given as 8 cm. So, the volume can be calculated as 8 cm * 8 cm * 8 cm = 512 cm3.
14.
Find the volume of the composite figure.
Correct Answer
A. 360 cm^{3}
Explanation
The volume of a composite figure is the sum of the volumes of its individual components. In this case, the given answer of 360 cm3 suggests that the volume of the composite figure is 360 cubic centimeters.
15.
What is the volume of the solid shown below?
Correct Answer
B. 255 in
16.
Which cylinder will have a larger volume?
Correct Answer
A. Cylinder A
Explanation
Cylinder A will have a larger volume because volume is calculated by multiplying the base area of the cylinder by its height. Since no specific measurements are given for either cylinder, we can assume that the base area and height of Cylinder A are larger than those of Cylinder B, resulting in a larger volume for Cylinder A.
17.
A sign made of solid wood is in the shape of a pyramid. The base is a triangle with a base of 6 feet and a height of 4 feet. The height of the sign is 7 feet. The wood costs $3 per cubic foot. What is the cost of the sign?
Correct Answer
C. $84
Explanation
The sign is in the shape of a pyramid, which means it can be divided into four congruent triangular pyramids. The volume of a triangular pyramid is given by the formula (1/3) * base * height. In this case, the base of each triangular pyramid is (1/2) * 6 * 4 = 12 square feet, and the height is 7 feet. Therefore, the volume of each triangular pyramid is (1/3) * 12 * 7 = 28 cubic feet. Since there are four triangular pyramids making up the sign, the total volume of the sign is 4 * 28 = 112 cubic feet. The cost of the sign is then calculated by multiplying the volume by the cost per cubic foot, which is 112 * 3 = $336. However, since the question is asking for the cost of the sign, we need to divide this by 4 (since there are four triangular pyramids) to get the final answer of $84.
18.
Find the total surface area of the prism.
Correct Answer
A. 161 square feet
19.
Find the surface area
Correct Answer
B. 188.4 m^{2}
20.
Dwayne Wade has recently bought a basketball for his son, Xavier. Since he's only 2, the basketball is quite small, measuring about 3 inches in diameter. What's the surface area of this ball?
Correct Answer
B. SA = 2πrh + 2πr^{2}
Explanation
The correct answer is SA = 2πrh + 2πr². This formula calculates the surface area of a ball. In this case, since the basketball is small with a diameter of 3 inches, the radius would be 3/2 = 1.5 inches. The formula includes two terms: 2πrh, which represents the curved surface area of the ball, and 2πr², which represents the surface area of the two circular ends of the ball. By plugging in the values for radius and height (which is not given in the question), we can calculate the surface area of the ball.