9514 1404 393
Answer:
- volume: 100π cm³ ≈ 314.2 cm³
- area: 65π cm² ≈ 204.2 cm²
Explanation:
The other leg of the right triangle is found from the Pythagorean theorem:
r² + 12² = 13²
r = √(169 -144) = √25 = 5
The solid of revolution is a cone with a radius of 5, a height of 12, and a slant height of 13.
The volume is given by ...
V = (1/3)πr²h
V = (1/3)π(5 cm)²(12 cm) = 100π cm³ . . . volume
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The lateral surface area is given by ...
LA = πrh . . . where h is the slant height
LA = π(5 cm)(13 cm) = 65π cm² . . . curved surface area