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Please calculate the volume of a solid oblique pyramid with a triangular base, given that the base has a length of 8 inches and a height of 6 inches, and the height of the pyramid is 10 inches. Round your answer to the nearest cubic inch.

User Nepete
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1 Answer

4 votes

Answer: 74

Explanation:

The volume of the pyramid can be found using the formula:

Volume = (1/3) x Base Area x Height

To find the base area, we need to find the area of the triangular base. The area of a triangle can be found using the formula:

Area = (1/2) x Base x Height

Substituting the given values, we have:

Area = (1/2) x 8 x 6 = 24 square inches

To find the height of the pyramid, we can use the Pythagorean theorem. The slant height and one-half of the base form a right triangle, so we have:

Height^2 = (Slant Height)^2 - (1/2 x Base)^2

Height^2 = 10^2 - 4^2

Height^2 = 84

Height = √84 ≈ 9.165 inches

Now we can substitute the values into the formula for the volume:

Volume = (1/3) x Base Area x Height

Volume = (1/3) x 24 x 9.165

Volume ≈ 73.96 cubic inches

Therefore, the volume of the pyramid is approximately 73.96 cubic inches.Step-by-step explanation:

User Rakesh Patel
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