The length of a side of the base of a pyramid is 3 cm, and the slant height is 7 cm. How much larger is the surface area of this pyramid than the surface area of a cone with a diameter of 3 cm and a slant height of 7 cm? Round to the nearest hundredth. A) 52.94 cm² B) 10.94 cm² C) 22.04 cm² D) 19.94 cm² E) 12.38 cm²

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Quizplus · Accepted Answer

The surface area of the pyramid is calculated by adding the area of the square base (3 cm x 3 cm = 9 cm²) and the area of the four triangular faces (4 x (1/2 x 3 cm x 7 cm) = 42 cm²), totaling 51 cm². The surface area of the cone is calculated by adding the area of the base (π x (1.5 cm)² ≈ 7.07 cm²) and the lateral surface area (π x 1.5 cm x 7 cm ≈ 32.99 cm²), totaling approximately 40.06 cm². The difference is 51 cm² - 40.06 cm² ≈ 10.94 cm².

The Length of a Side of the Base of a Pyramid