The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm². If the volume of metal used in making the cylinder is 176 cm³, find the outer and inner diameters of the cylinder. (Use π = 22/7)

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Solution

The height of the hollow cylinder is 14 cm. Let the inner and outer radii of the hollow cylinder are r cm and R cm respectively. The difference between the outer and inner surface area of the hollow cylinder is

By the given condition, this difference is 88 square cm. Hence, we have

The volume of the metal used in making the cylinder is

By the given condition, the volume of the metal is 176 cubic cm. Hence, we have

Hence, we have two equations with unknowns R and r

Adding the two equations, we have

Then from the second equation, we have

Therefore, the outer and inner diameters of the hollow cylinder are 5cm and 3cm respectively.

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