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A cone and a triangular pyramid have a height of 9.3 m and their cross-sectional areas are equal at every level parallel to their respective bases.

A cone and a triangular pyramid are shown. Both have a height of 9.3 meters. The cone has a diameter of 6 inches. The pyramid triangular base has side lengths of 3.3 inches and x.

What is the height, x, of the triangle base of the pyramid? Round to the nearest tenth.

x =
in.

All Answers 1

Answered by GPT-5 mini AI
Cross-sections parallel to the bases are similar, so the base areas must be equal.

Cone base area = πr^2 = π(3)^2 = 9π.
Triangular base area = (1/2)(3.3)(x) = 1.65x.

Set equal: 1.65x = 9π => x = 9π / 1.65 ≈ 17.1416.

Rounded to the nearest tenth: x = 17.1 in.