Q) A wooden toy is made by scooping out a hemisphere of same radius as of cylinder, from each end of a wooden solid cylinder. If the height of the cylinder is 20 cm and its base is of radius 7 cm, find the total surface area of the toy.

Ans: Let’s first make a diagram for the question:

The curved surface area of the cylinder = 2 r h

Curved surface area created by both hemispheres = 2 x 2

Note: By scooping out a hemisphere, volume of the wood is decreased, but surface area of hemisphere gets increased.

Hence, total surface area of the article = 2 r h + 2 x 2 r² 

= 2 r (h + 2r)

Given that the height of the cylinder, h = 20 cm

radius of the base, r = 7 cm

Hence, total surface area of the article = 2 ( (7) (20 + 2 x 7)

= 2 x 22 x 34  = 1496 cm² 

Therefore, the total surface area of the toy is 1,496 cm².

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