Grade 8-Surface Area and Volume

Calculate the surface area of a swimming pool with side length 5 meters.

• 25 square meters

• 40 square meters

• 30 square meters

• 150 square meters

Answer explanation

The surface area of a swimming pool with side length 5 meters is calculated by multiplying the length of one side by itself, and then multiplying the result by 6. Therefore, the surface area is 5 * 5 * 6 = 150 square meters. This is the correct choice.

Find the volume of a swimming pool with length 8 meters, width 4 meters, and depth 3 meters.

• 32 cubic meters

• 48 cubic meters

• 64 cubic meters

• 96 cubic meters

Answer explanation

The volume of a swimming pool can be calculated by multiplying its length, width, and depth. In this case, the volume is 8 meters * 4 meters * 3 meters = 96 cubic meters. Therefore, the correct answer is 96 cubic meters.

Using the formula 2πr(r+h), calculate the surface area of a cylinder with radius 6 cm and height 10 cm.

• 452.39 cm²

• 301.59 cm²

• 528.34 cm²

• 94.25 cm²

Answer explanation

The surface area of a cylinder can be calculated using the formula 2πr(r+h). Plugging in the values, we get 2π(6)(6+10) = 2π(6)(16) = 192π ≈ 452.39 cm². Therefore, the correct answer is 452.39 cm².

Determine the volume of a sphere with radius 12 cm. (Use the formula V = 4/3πr^3)

• 6012.45 cm^3

• 144.76 cm^3

• 2895.12 cm^3

• 7238.23 cm^3

Answer explanation

The volume of a sphere with a radius of 12 cm can be calculated using the formula V = 4/3πr^3. Plugging in the value of the radius, we get V = 4/3π(12^3) = 7238.23 cm^3. Therefore, the correct answer is 7238.23 cm^3.

A construction company is building a rectangular pyramid with a base area of 20 cm² and a height of 9 cm. What is the volume of the pyramid?

• 45 cm³

• 60 cm³

• 180 cm³

• 120 cm³

Answer explanation

The volume of a pyramid is calculated by multiplying the base area by the height and dividing by 3. In this case, the volume is (20 cm² * 9 cm) / 3 = 60 cm³. Therefore, the correct answer is 60 cm³.

A fish tank has dimensions 30 cm x 15 cm x 20 cm. What is the total surface area of the tank?

• 1350 cm^2

• 450 cm^2

• 900 cm^2

• 600 cm^2

Answer explanation

The total surface area of the fish tank can be calculated by finding the sum of the areas of all its sides. Since the tank has dimensions of 30 cm x 15 cm x 20 cm, the total surface area is 2(30x15) + 2(30x20) + 2(15x20) = 1350 cm^2. Therefore, the correct answer is 1350 cm^2.

A cylindrical container has a radius of 5 cm and a height of 12 cm. What is the volume of the container?

• 60.24 cm³

• 25 cm³

• 314.16 cm³

• 150.72 cm³

Answer explanation

The volume of a cylinder is calculated by multiplying the area of the base (πr²) by the height. The correct choice, 314.16 cm³, is obtained by substituting the given values into the formula: π(5²)(12) = 314.16 cm³.

If a cube has a surface area of 150 cm², what is the length of each side?

• 25 cm

• 5 cm

• 10 cm

• 3 cm

Answer explanation

The surface area of a cube is given by 6 * (side length)^2. To find the length of each side, we can rearrange the formula as side length = sqrt(surface area / 6). Plugging in the given surface area of 150 cm², we get side length = sqrt(150 / 6) = 5 cm. Therefore, the length of each side is 5 cm, which matches the correct answer choice.

A traffic cone has a radius of 8 cm and a slant height of 10 cm. Calculate its surface area. (Use the formula A = πr(r + l))

• 40.84 cm²

• 628.32 cm²

• 314.16 cm²

• 72.56 cm²

Answer explanation

The surface area of a traffic cone can be calculated using the formula A = πr(r + l). Plugging in the values, we get A = π(8)(8 + 10) = 314.16 cm². Therefore, the correct answer is 314.16 cm².

A water tank has a volume of 288π cm³. What is the radius of the tank?

• 12 cm

• 6 cm

• 10 cm

• 4 cm

Answer explanation

The volume of a sphere is given by the formula V = (4/3)πr³. Solving for r, we get r = (3V/4π)^(1/3). Substituting the given volume, we find r = (3(288π)/4π)^(1/3) = 6 cm. Therefore, the radius of the tank is 6 cm, which matches the correct answer choice.