Question

pyramid a is a square pyramid with a base side length of 7 inches and a height of 8 inches. pyramid b has a volume of 3,136 in³. how many times bigger is the volume of pyramid b than pyramid a?

Explanation:

Step1: Calculate volume of pyramid A

The volume formula for a square - pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height. The base of pyramid A is a square with side length $7$ inches, so $B = 7\times7=49$ square inches, and $h = 8$ inches. Then $V_A=\frac{1}{3}\times49\times8=\frac{392}{3}$ $in^3$.

Step2: Find the ratio of volumes

We know $V_B = 3136$ $in^3$. To find how many times bigger $V_B$ is than $V_A$, we calculate the ratio $\frac{V_B}{V_A}$. Substitute $V_A=\frac{392}{3}$ and $V_B = 3136$ into the ratio: $\frac{3136}{\frac{392}{3}}=3136\times\frac{3}{392}=24$.

Answer:

24