Question

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

• A. $54$
• B. $15$
• C. $27$
• D. $75$

Answer 1

The correct option is C

$27$

Explanation for the correct option:

Step-1: Solve for the volume of square pyramids:

We know that the volume of the square pyramid is: $V={\left(s\right)}^2\times \frac{h}{3}$, where $s=$side length and $h=$ height.

Given that the pyramid $A$ is a square pyramid with a base side length of $12inches$ and a height of $8inches$ and the pyramid $B$ is a square pyramid with a base side length of $36inches$ and a height of $24inches$.

So, Volume of pyramid $A$ is$V_A={\left(12\right)}^2\times \frac{8}{3}i{n}^3$

and Volume of pyramid $B$ is$V_B={\left(36\right)}^2\times \frac{24}{3}i{n}^3$

Step-2: Solve for the required value:

The number of times the volume of pyramid $B$ is bigger than pyramid $A$$=\frac{V_B}{V_A}$

$$\begin{gathered} =\frac{{\left(36\right)}^2\times {\displaystyle \frac{24}{3}}}{{\left(12\right)}^2\times {\displaystyle \frac{8}{3}}} \\ =\frac{36\times 36\times 24}{12\times 12\times 8} \\ =3\times 3\times 3 \\ =27 \end{gathered}$$

Therefore, the volume of pyramid $B$ is $27$ times bigger than that of pyramid $A$.

Hence, option(C) is the correct answer.