Question

right circular cylinder and a right circular cone have equal bases and equal volumes but the lateral surface area of right circular cone is 15/ 8 times the lateral surface area of the right circular cylinder what is the ratio of radius to height of the cylinder

Answer 1

Given:

• Right circular cylinder and a right circular cone have equal bases and equal volumes.
• The lateral surface area of right circular cone is 15/ 8 times the lateral surface area of the right circular cylinder.

To Find:

 The ratio of radius to height of the cylinder.

Solution:

1) Parameters of the cylinder:

• Radius- R

• Height-h

2) Parameters of the cone:

• Radius- R

• Height- H

• Slant height- L

3) Bases of the cone and cylinder are same means the radius will be same of both.

4) It is given in the question that the volume of the cone and cylinder are same.

• V1 = V2

• 1/3πR²H = πR²h

• H = 3h

5) The lateral surface area of right circular cone is 15/ 8 times the lateral surface area of the right circular cylinder.

• A1 = 15/8A2

• πRL = 15/8×2×πRh

• L=15/4h

6) We all are very aware by the formula:

• L²=H²+R²

• (15/4h)² = (3h)² + R²

• 225/16h²-9h² = R²

• (81/16)h² = R²

• R/h=√(81/16)

• R/h = 9/4

The ratio of radius to height of the cylinder is 9:4.

Answer 2

Step-by-step explanation:

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