Question

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The volume of a square pyramid with a height of 12 m is 100 m³. Find the length of its square base.

Answer 1

V = Ab·h : 3

100m³ = Ab·12m : 3

300m³ = Ab·12m

Ab = 300m³/12m

= 25m²

Ab = 25m² = L²

L = √25m²

L = 5m

Answer 2

5 m

Explanation:

The volume (V) of a square based pyramid is

V =
`(1)/(3)` Ah ( A is the area of base and h the height ), thus

`(1)/(3)` A × 12 = 100, that is

4A = 100 ( divide both sides by 4 )

A = 25

Hence s² = 25 ← s is the side of square base

Take the square root of both sides

s =
`√(25)` = 5