Question

Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with a base side length of 36 inches and a height of 24 inches. How many times bigger is the volume of pyramid B than pyramid A?

Answer 1

Answer:

27 times

Step-by-step explanation:

The formula of a volume of a pyramid:

$V=\dfrac{1}{3}BH$

B - base area

H - height

We have two square pyramids.

The bases are squares. The formula of an area of a square with sides s :

$A=s^2$

Pyramid A:

s = 12in, H = 8in

$B_A=12^2=144\ in^2\\\\V_A=\dfrac{1}{3}(144)(8)=384\ in^3$

Pyramid B:

s = 36in, H = 24in

$B_B=36^2=1296\ in^2\\\\V_B=\dfrac{1}{3}(1296)(24)=10368\ in^3$

Calculate the quotient:

$\dfrac{V_B}{V_A}=\dfrac{10368}{384}=27$