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

Algebra ->  Surface-area -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


The lateral surface area is %28pi%29%28r%29%28l%29 where l is the slant height.

With a radius of 10 and a height of 30, the slant height is sqrt%2810%5E2%2B30%5E2%29+=+sqrt%281000%29+=+10sqrt%2810%29

Then the lateral surface area is %28pi%29%2810%29%2810sqrt%2810%29%29+=+100pi%2Asqrt%2810%29

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 100pi%2A%284%2F9%29+=+400pi%2F9.