MATH 6 Q4

If a pyramid and a prism have congruent bases and equal heights, what is the relationship between their volumes?

• The volume of the pyramid is ⅔ of the volume of the prism.

• The volume of the pyramid is 3/3 of the volume of the prism.

• The volume of the pyramid is 1/3 of the volume of the prism.

• The volume of the pyramid is 3/2 of the volume of the prism.

If a cylinder and a cone have congruent bases and equal heights, how many times greater is the cylinder's volume compared to the cone's volume?

• double

• thrice

• twice

• 4 times

How many cones can exactly fill a sphere of the same radius and height?

• 1

• 2

• 3

• 4

A cylinder has a volume of 120 m³. What is the volume of a cone with the same base and height as the cylinder?

• 180m³

• 60m³

• 40m³

• 30m³

What is the length of the edge of a cube if it has a volume of 27 cubic inches?

• 9 in

• 6 in

• 3 in

• 2in

The length of each side of a cube is 10 cm. What is the volume?

• 1000cm³

• 500cm³

• 300cm³

• 100cm³

A gardener is planning to fill a rectangular plant box with soil. The plant box has dimensions of 4 cm × 10 cm × 5 cm. The gardener claims that 250 cm³ of soil will be enough to completely fill the box. Is the gardener's claim correct? Justify your answer by calculating the actual volume of the plant box.

• Yes, because the plant box holds exactly 250 cm³ of soil.

• No, because the plant box requires more than 250 cm³ of soil.

• No, because the plant box requires less than 250 cm³ of soil.

• Yes, because any amount of soil can fill the box.

A rectangular swimming pool measures 25 m by 16 m, with an average depth of 4 m. How many cubic meters of water are needed to fill the pool?

• 1700m³

• 1600m³

• 1500m³

• 1400m³

What is the volume of the illustrated pyramid?

• 600in³

• 500in³

• 400in³

• 300in³

A student calculated the volume of a square pyramid with a base area of 22.5 m² and a height of 5 m. The student claimed the answer was 37.5 m³. Evaluate whether this answer is correct and justify your reasoning.

• Incorrect! The student forgot to multiply by 1/3, leading to an overestimation.

• Incorrect! The volume of this pyramid should be less than 30 m³ because pyramids always have smaller volumes than expected.

• Correct! The student correctly applied the volume formula 푉 = 1/3퐵ℎ, where 퐵=22.5, and h=5.

• Cannot be determined. Without knowing the slant height, the volume cannot be confirmed.