Question

Cylinder A has a radius of 6 feet and a height that is 5.5 feet less than Cylinder B. Cylinder b has a radius of 4. The cylinders have the same surface area. Find the height of each cylinder.

Answer 1

Considering the equation for the surface area of a cylinder, we have that the heights are given as follows:

• Cylinder A: 1 feet.

• Cylinder B: 6.5 feet.

What is the surface area of a cylinder?

The surface area of a cylinder of radius r and height h is given by the following equation:

S = 2πr(r + h).

In this problem, we have that:

• Cylinder A has radius r = 6 and height h = h - 5.5.

• Cylinder B has radius r = 4 and height h.

They have the same surface areas, hence:

12π(6 + h - 5.5) = 8π(4 + h)

12(0.5 + h) = 32 + 8h

6 + 12h = 32 + 8h

4h = 26

h = 6.5.

Hence the heights are given as follows:

• Cylinder A: 1 feet.

• Cylinder B: 6.5 feet.

More can be learned about the surface area of a cylinder at https://brainly.com/question/26702574

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