The radius and height of a cone are reduced by the same factor of 6. If the original surface area was 213.3, the new surface area. Round your answer to the nearest hundredth

Question

The radius and height of a cone are reduced by the same factor of 6. If the original surface area was 213.3, the new surface area. Round your answer to the nearest hundredth

Answer 1

If a new figure is enlarged or reduced by a factor of k, the area will be changed by a factor of k² and the volume will be changed by a factor of k³. If the radius and height of a cone are reduced by a factor of 6, then the scale factor is k = 1/6. The surface area of the reduced cone will be reduced by k² = (1/6)² = 1/36, so multiply the original surface area by 1/36 ( or just divide it by 36) to get the surface area of the reduced cone.