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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?

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 tha class=

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mhanifa

Answer:

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

Step-by-step 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:

  • [tex]S_A = 2\pi r(h + r)[/tex]

Total surface area of cylinder B is:

  • [tex]S_B = 2\pi(4r)(4r + 4h) = 8\pi(4)(r + h) = 32\pi(r + h)[/tex]

Find the ratio of areas:

  • [tex]\cfrac{S_B}{S_A} =\cfrac{32\pi(r+h)}{2\pi(r+h)} =16[/tex]

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