Multiple choice

A solid is in the form of a cylinder with hemispherical ends. If the height of the solid is 26cm and diameter of cylindrical part is 14 cm, then find the cost of covering the solid with metal sheet (Cost of metal sheet is Rs.15/cm²).

  1. Rs.16570

  2. Rs.15440

  3. Rs.17160

  4. Rs.12420

  5. Rs.14370
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cylinder height = 26 - 7 - 7 = 12 cm. Radius = 7 cm. Surface area = 2*pi*r*h (cylinder) + 4*pi*r^2 (two hemispheres) = 2*pi*7*12 + 4*pi*49 = 168*pi + 196*pi = 364*pi. 364 * 3.14159 * 15 = 17153. The closest option is 17160.

AI explanation

The radius is 7 cm, and since the total height is 26 cm, the cylindrical portion's height is 26 minus 14, which is 12 cm. The total surface area consists of the curved surface of the cylinder and the curved surfaces of the two hemispheres, calculated as 2 times pi times 7 times 12 plus 4 times pi times 7 squared. Using 22 divided by 7 for pi results in a total surface area of 1144 square cm. Multiplying this area by the cost of 15 gives Rs. 17160.

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