Volumes REview

Anika is making a decorative cone for a school project. Calculate the volume of the cone if it is expected to be

150.72 cm³

.

• 150.72 cm³

• 75.36 cm³

• 452.16 cm³

• 151 cm³

Answer explanation

To find the volume of a cone, use the formula V = (1/3) * π * r² * h. Substituting the values (r=6 cm, h=5 cm) gives V = (1/3) * π * 6² * 5 ≈ 150.72 cm³. Therefore, the correct answer is 150.72 cm³.

Maya is designing a garden with a decorative spherical fountain at its center. Calculate the volume of the sphere that forms the fountain.

• 78.5 m³

• 392.5 m³

• 523.6 m³

• 62.8 cm³

Answer explanation

The volume of a sphere is calculated using the formula V = (4/3)πr^3. Given the radius, the volume is V = (4/3)π(10)^3 = 523.6 m^3.

Mia is planning a geography project and needs to calculate the volume of a model globe that has a radius of 11 inches. How much space does the globe occupy?

• 523 in³

• 16,717 in³

• 5,575 in³

• 7,235 in³

Answer explanation

To find the volume of a sphere, use the formula V = (4/3)πr^3. Substituting r=11, V = (4/3)π(11)^3 = 5575 in^3. Therefore, the correct answer is 5,575 in^3.

Charlotte is crafting a cylindrical vase with a height of 10 cm and a radius of 3 cm. What is the volume of the vase?

• 250

• 200

• 283

• 180

Answer explanation

The formula for the volume of a cylinder is V = πr^2h. Substituting r=3 and h=10, V = π(3^2)(10) = 283. Therefore, the correct answer is 283.

Emma is designing a garden with a decorative cone-shaped fountain that has a diameter of 8 feet and a height of 3 feet. Calculate the volume of this fountain.

Answer explanation

The volume of a cone is calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius. Given the diameter is 8 feet, the radius is 4 feet. Substituting the values, V = (1/3) * π * 4^2 * 3 = 16π ft3.

Ethan is building a water storage tank in the shape of a cylinder with a height of 4 m and a diameter of 4 m. What is the volume of the tank?

• 64π m³

• 16π m³

• 64π m²

• 16π m²

Answer explanation

The volume of a cylinder is calculated using the formula V = πr^2h. Given the diameter is 4m, the radius is 2m. Substituting r=2 and h=4 into the formula gives V = π(2)^2(4) = 16π m^3.

Ethan is playing table tennis and wonders about the volume of the ball he is using. The ball has a diameter of 40 mm. What is the exact volume of this table tennis ball in cubic millimeters?

• 33,510.3 mm³

• 268,083 mm³

Answer explanation

The correct choice is 10,666 2/3π mm3. The formula for the volume of a sphere is V = (4/3)πr^3. Substituting the radius (20 mm) into the formula gives V = (4/3)π(20)^3 = 10,666 2/3π mm3.

Mike has a large plastic cup in the shape of a cone, which he uses to measure ingredients for his cooking. He is about to fill it with water to check its volume. Which is closest to the volume of Mike's cup?

• 21 cubic inches

• 63 cubic inches

• 66 cubic inches

• 198 cubic inches

Answer explanation

The volume of a cone is (1/3) * π * r^2 * h. Given r=3 and h=6, the volume is (1/3) * π * 3^2 * 6 = 66 cubic inches, which is closest to the volume of Mike's cup.

Daniel is working on a project to design water tanks for a community garden. He needs to choose a tank with a volume of 45π ft³. Which tank should he select?

• Cylinder with a height of 5ft and diameter of 6 ft

• Sphere with a radius of 3 ft

• Cone with a radius of 3 feet and height of 5 ft

• Sphere with a diameter of 5 feet

Answer explanation

The figure with a volume of 45π ft^3 is a cylinder with a height of 5ft and diameter of 6 ft, as V = πr^2h = 45π ft^3.

Kai is designing a unique water tank for a school project, which is composed of a rectangular prism and two half cylinders attached on top. Which is closest to the volume of the tank?

• 781 cm³

• 706 cm³

• 631 cm³

• 593 cm³

Answer explanation

The closest volume to the figure is 706 cm^3, as it is the most accurate approximation based on the given shape.