Question

Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?

Answer 1

The height of the second square base prism is 50 cm.

How to find volume of a square base prism?

The volume of the first square base prism is represented as follows:

v = ha²

where

• h = height

• a = side length of the base

Therefore, the height of the prism is 10 cm.

v = 10a²

Hence, the volume of the initial prism is 5 times the volume. Therefore,

v = 5(10a²)

v = 50a²

Therefore,

50a² = ha²

divide both sides by a²

50a² / a² = ha² / a²

50 = h

h = 50  cm

Therefore, the height of the second square base prism is 50 cm.

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