Answer:
A. 1160.0 square feet
B. 646.3 square inches
Explanation:
You want the surface area of the cone and the hexagonal pyramid shown.
A. Cone
The formula for the surface area of the cone makes use of the slant height. We can figure that using the Pythagorean theorem.
s² = r² +h²
s = √(10² +25²) = √725 ≈ 26.926 . . . . feet
The area is ...
A = πr(r +s) = π(10 ft)(10 ft +26.926 ft) ≈ 1160.0 ft²
The surface area of the cone is about 1160.0 square feet.
B. Pyramid
The base area is that of 6 equilateral triangles, each of which has a height of (8 in)(√3/2) = 4√3 in.
The total area is 6 times the area of one of the base triangles and one of the face triangles:
A = 6(1/2b(h1 +h2)) = 3(8 in)(4√3 in + 20 in) ≈ 646.3 in²
The surface area of the pyramid is about 646.3 square inches.
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