Advanced Area and Volume Calculations

What is the formula for the volume of a sphere?

How does a cone's volume compare to a cylinder with the same base and height?

• It is the same

• It is ½ the volume

• It is ¼ the volume

• It is ⅓ the volume

Which 3D shape does not have a flat surface in its net?

• Cube

• Cylinder

• Pyramid

• Sphere

A cube has a side length of 6 cm. If the side length doubles, how does its volume change?

• It doubles

• It increases 8 times

• It increases 6 times

• It increases 4 times

A hemisphere has a radius of 3 in. What is its volume? (Use π ≈ 3.14)

• 56.52 in³

• 113.04 in³

• 169.56 in³

• 226.08 in³

How do we calculate the lateral surface area of a cone?

If a solid has a base area of 25 cm² and a height of 10 cm, what is the volume of a prism with these dimensions?

• 50 cm³

• 100 cm³

• 250 cm³

• 500 cm³

What happens to the volume of a shape when scaled by a factor of 3?

• It triples

• It increases 6 times

• It increases 9 times

• It increases 27 times

A cone has a slant height of 10 cm and base radius of 6 cm. What is its lateral surface area?

• 60π cm²

• 20π cm²

• 30π cm²

• 100π cm²