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 48 inches and a height of 32 inches. How many times bigger is the volume of pyramid B than pyramid A? (4 points) I got 4 for this, im unsure if I got this correct

Answer 1

Answer:

The volume of pyramid B is 64 times the volume of pyramid A.

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, $s_A =$ 12 inches

Height of A, $h_A =$ 8 inches

Side Length of B, $s_B =$ 48 inches

Height of B, $h_B =$ 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

OR

$V_B$ is how many times bigger than $V_A$ ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

$V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}$

Here, base is square, so:

$V=\dfrac{1}{3} \times s^2 \times h$

Volume of pyramid A:

$V_A=\dfrac{1}{3} \times s_A^2 \times h_A$

$\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3$

Volume of pyramid B:

$V_B=\dfrac{1}{3} \times s_B^2 \times h_B$

$\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3$

The volume of pyramid B is 64 times the volume of pyramid A.