Question

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

Answer 1

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.

Answer 2

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)