SOLUTION: A right circular cone has a base radius of 10 cm and an altitude of 30 cm. Find the lateral area of the cone.Find the area of cross-section 20 cm from the vertex if area one is equ
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Question 1116875: A right circular cone has a base radius of 10 cm and an altitude of 30 cm. Find the lateral area of the cone.Find the area of cross-section 20 cm from the vertex if area one is equal to 100 pi.
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!
The lateral surface area is where l is the slant height.
With a radius of 10 and a height of 30, the slant height is
Then the lateral surface area is
Think of the cross section 20cm from the vertex as the base of a cone with the same vertex as the original cone and a height of 20cm instead of 30cm. The two cones will be similar, with a scale factor of 20/30 = 2/3. That means the ratio of corresponding areas will be 2^2/3^2 = 4/9. So the area of the cross section 20cm from the vertex is .
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