Question

Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 4r and height 4h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?

Answer 1

• The surface area of Cylinder B is 16 times the surface area of Cylinder A

Explanation:

Note: It is assumed we are looking at the total surface area (but the answer would be same for both cases)

Given

• Cylinders A with radius - r, height - h,
• Cylinder B with radius - 4r, height - 4h.

To find

• The ratio of total surface areas of cylinder B to A

Solution

Total surface area of cylinder A is:

• 
  `S_A = 2\pi r(h + r)`

Total surface area of cylinder B is:

• 
  `S_B = 2\pi(4r)(4r + 4h) = 8\pi(4)(r + h) = 32\pi(r + h)`

Find the ratio of areas:

• 
  `\cfrac{S_B}{S_A} =\cfrac{32\pi(r+h)}{2\pi(r+h)} =16`