Question

Consider a regular pyramid A with a square base and a right circular cone B.

It is given that the length of a side of the square base of pyramid A is the same as the base radius of cone B.

If the two solids have the same volume, which solid will have a greater height? Explain your answer.

Please help me solve this question with steps!orz​

Answer 1

Pyramid

Explanation:

`\text{Volume of a Square Pyramid }=(1)/(3) * l^2 * Height\\\\ \text{Volume of a Cone }=(1)/(3) \pi r^2 * Height`

Given that the two solids have the same volume

`(1)/(3) * l^2 * Height=(1)/(3) \pi r^2 * Height`

If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r

`(1)/(3) * l^2 * $Height of Pyramid=$(1)/(3) \pi l^2 * $Height of cone$\\\\$Cancel out $ (1)/(3) * l^2$ on both sides\\\\Height of Pyramid= \pi * $ Height of cone$`

If the height of the cone is 1

`H$eight of Pyramid= \pi * 1 \approx 3.14$ units`

Therefore, the pyramid has a greater height.