Question

A pyramid has a base with an area of 25 in² and a

volume of 100 in³. Find the height of the pyramid.

Answer 1

12in

Explanation:

Area and Volume (Proportion)

Base Area and Volume are proportionalised based on their Height.

Eg. Base Area of Cube = Length × Width

Volume of Cube = Length × Width × Height

Solution

Given from the Question:

Base Area of Pyramid =

`25 \: {in}^(2)`

Volume of Pyramid =

`(1)/(3) (base \: area)(height) = 100 {in}^(2)`

We already knew the Base Area, so we can substitute it into the Volume of Pyramid Formula to find the height.

`(1)/(3) (25)(height) = 100 \\ height = (100(3))/(25) \\ = 12in`

Therefore the height of the Pyramid is 12in.