Problem

The Jones family is going camping next weekend. They plan to sleep in a tent that is in the shape of a squarebased pyramid. The square base has sides of length 11 feet and a height of 8 feet. How many cubic feet are 27 available inside the pyramid? Round your answer to the nearest cubic foot. 30

Solution

Step 1 :The Jones family is going camping next weekend. They plan to sleep in a tent that is in the shape of a square-based pyramid. The square base has sides of length 11 feet and a height of 8 feet. We are asked to find how many cubic feet are available inside the pyramid, rounding our answer to the nearest cubic foot.

Step 2 :The volume of a pyramid is given by the formula \(V = \frac{1}{3} \times \text{base area} \times \text{height}\). In this case, the base is a square with side length 11 feet, so the base area is \(11 \times 11 = 121\) square feet. The height is 8 feet.

Step 3 :We can calculate the volume by substituting these values into the formula: \(V = \frac{1}{3} \times 121 \times 8\).

Step 4 :This gives us a volume of approximately 322.66666666666663 cubic feet.

Step 5 :Rounding to the nearest cubic foot, we get a final volume of 323 cubic feet.

Step 6 :Final Answer: The volume of the pyramid is approximately \(\boxed{323}\) cubic feet.

From Solvely APP
Source: https://solvelyapp.com/problems/20415/

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