Question

question 9 multiple choice worth 1 points (05.02 mc) pyramid a is a square pyramid with a base side length of 9 inches and a height of 4 inches. pyramid b has a volume of 8,100 in³. how many times bigger is the volume of pyramid b than pyramid a?
options: 15, 32, 54, 75

Explanation:

Step1: Calculate Volume of Pyramid A

The formula for the volume of a square pyramid is $V = \frac{1}{3}s^2h$, where $s$ is the base side length and $h$ is the height. For Pyramid A, $s = 9$ inches and $h = 4$ inches.
$$V_A=\frac{1}{3}\times9^2\times4=\frac{1}{3}\times81\times4 = 27\times4 = 108\ \text{in}^3$$

Step2: Find the Ratio of Volumes

We know the volume of Pyramid B, $V_B = 8100\ \text{in}^3$. To find how many times bigger $V_B$ is than $V_A$, we calculate the ratio $\frac{V_B}{V_A}$.
$$\frac{V_B}{V_A}=\frac{8100}{108}=75$$

Answer:

75 (corresponding to the option with 75)