Question

A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.​

Answer 1

• The radius of the container is approximately 4.89 cm

Explanation:

Given

A container with:

• r = h
• S = 300 cm²

To find

• The radius of the container

Solution

Use the equation for total surface area of cylinder:

• S = 2πr² + 2πrh or S = 2πr(r + h)

Since we have r = h and the value of S is known, let's solve this equation:

• 2πr(r + h) = 300
• 2πr(r + r) = 300
• 2πr(2r) = 300
• 4πr² = 300
• πr² = 75
• 3.14r² = 75
• r² = 75/3.14
• r² = 23.89 (rounded)
• r = √23.89
• r = 4.89 cm (rounded)