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Two similar pyramids have lateral areas 20ft2 and 45ft2. The volume of the smaller pyramid is 8ft3.

What is the volume of the larger pyramid?

A27ft3
B18ft3
C36ft3
D9ft3

Verified Answer :

syed514

Let the ratio between 2 of them be a/b. The volume of the larger one is x (ft^3) 
(a/b)^2 = 20/45 = 4/9 ---> a/b = 2/3 
(a/b)^3 = 8/x 
8/x = (2/3)^3 = 8/27 ---> x = 27 (ft^3) 

Answer:  Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Lateral surface area of smaller pyramid = 20 ft²

Lateral surface area of larger pyramid = 45 ft²

volume of smaller pyramid  = 8 ft³

We need to find the volume of larger pyramid.

\(\dfrac{\text{Lateral area of smaller pyramid}}{\text{Lateral area of larger pyramid}}=\dfrac{20}{45}=\dfrac{4}{9}\\\\\dfrac{4}{9}=\dfrac{2^2}{3^3}\\\\\dfrac{\text{side of smaller pyramid}}{\text{Side of larger pyramid}}=\dfrac{2}{3}\\\\So,\\\\\dfrac{\text{Volume of smaller pyramid}}{\text{Volume of larger pyramid}}=\dfrac{2^3}{3^3}=\dfrac{8}{27}\)

Hence, Volume of larger pyramid is 27 ft³.

Therefore, Option 'A' is correct.

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