Use what you know about the volume of pyramids to solve the following problem: The capacity of a square-pyramid-shaped camping tent is 308,025 in.3. When fully pitched, the tent has a height of 75 in. What is the length of each side of the tent’s base? Round to the nearest tenth.
Responses:
111.0 in.
12,321.0 in.
55.5 in.
64.1 in.
To find the length of each side of the tent's base, we need to first calculate the volume of the pyramid using the formula V = (1/3) * l * w * h, where l and w are the dimensions of the base and h is the height of the pyramid.
Given:
V = 308,025 in^3
h = 75 in
Using the formula, we get:
308,025 = (1/3) * l * w * 75
l * w = 308,025 * 3 / 75
l * w = 12,321
Since the tent is square-based, l = w. Therefore, we can rewrite the equation as:
l^2 = 12,321
l = √12,321
l ≈ 111 in
Therefore, the length of each side of the tent's base is approximately 111 in.
So, the correct response is:
111.0 in.