Question

Danny is measuring two pyramids whose bases are squares. Given the height and volume V of the first pyramid, Danny uses the formula

a=√(3V/h)
to compute its base's side length a to be 5 meters. The second pyramid has the same volume, but has 4 times the height. What is the side length of its base?

Answer 1

Given that the first pyramid has a base side length of 5 meters and the second pyramid has the same volume but 4 times the height, the side length of the base of the second pyramid is found to be 2.5 meters.

Step-by-step explanation:

The student has provided the formula a=√(3V/h) for calculating the side length a of a pyramid's base when the volume V and height h are known. Given that the first pyramid's base side length is 5 meters and the second pyramid has 4 times the height of the first but the same volume, we can calculate the second pyramid's base side length.

For the first pyramid, the side length a is found to be 5 meters using the formula, which means:

5 = √(3V/h)

This implies:

25 = 3V/h

The volume V thus equals (25h/3).

The second pyramid has the same volume V but 4 times the height (4h). Using the formula:

a' = √(3V/(4h))

= √(3*(25h/3)/(4h))

= √(25/4)

Therefore, the side length of the base a' for the second pyramid is √(6.25) or 2.5 meters.