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

Answer:

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

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

$V=\frac{1}{3}Bh$

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

$V=\frac{1}{3}B(10)$

$V=\frac{10}{3}B\ cm^{3}$

Find the volume of the larger model

we have

$h=30\ cm$

substitute

$V=\frac{1}{3}B(30)$

$V=\frac{30}{3}B=10B\ cm^{3}$

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

$10B/(\frac{10}{3}B)=3$

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