Question

Two architectural models are pyramids with bases of equal area. The smaller model has a height of 10 centimeters, and the larger model has a height of 30 centimeters. How many times greater than the smaller model is the larger model’s volume?

Answer 1

The larger model’s volume is 3 times greater than the volume of the smaller model

Explanation:

we know that

The volume of a pyramid is equal to

`V=(1)/(3)Bh`

where

B is the area of the base of pyramid

h is the height of the pyramid

Find the volume of the smaller model

we have

`h=10\ cm`

substitute

`V=(1)/(3)B(10)`

`V=(10)/(3)B\ cm^(3)`

Find the volume of the larger model

we have

`h=30\ cm`

substitute

`V=(1)/(3)B(30)`

`V=(30)/(3)B=10B\ cm^(3)`

To find how many times greater than the smaller model is the larger model’s volume, divide the volume of the larger model by the volume of the smaller model

so

`10B/((10)/(3)B)=3`

The larger model’s volume is 3 times greater than the volume of the smaller model