Multiple choice

A hollow cylinder is made up of metal. The difference between the outer and inner curved surface areas of this cylinder is 352 cm2. Height of the cylinder is 28 cm. If the total surface area of this hollow cylinder is 2640 cm2, then what are the inner and outer radii (in cm)?

  1. 4, 6

  2. 10, 12

  3. 8, 10

  4. 6, 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R be the outer radius and r be the inner radius. Difference in curved surface areas: 2*pi*h*(R-r) = 352. 2*(22/7)28(R-r) = 352 => 176*(R-r) = 352 => R-r = 2. Total surface area: 2*pi*(R+r)h + 2*pi(R^2-r^2) = 2640. 2*pi*(R+r)28 + 2*pi(R-r)(R+r) = 2640. 2*pi*(R+r)(28+2) = 2640 => 2(22/7)*(R+r)*30 = 2640 => (R+r) = 2640 * 7 / (44 * 30) = 14. Solving R-r=2 and R+r=14 gives R=8, r=6.

AI explanation

The difference between the outer and inner curved surface areas gives 2 times pi times height times (R minus r), which simplifies as 2 times 22 divided by 7 times 28 times (R minus r) equals 352; solving this gives R minus r equals 2. The total surface area formula is 2 times pi times (R plus r) times (height plus R minus r), so 2 times 22 divided by 7 times (28 plus 2) times 2 equals 2640; solving this gives R plus r equals 14. Solving the two equations reveals the inner and outer radii are 6 centimeters and 8 centimeters.

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