Q) A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5·8 cm and its base is of radius 2·1 cm, find the total surface area of the article.

Ans: 

Let’s make a diagram marking all the given dimensions:

The curved surface area of the cylinder = 2 r h

Curved surface area created by both hemispheres = 2 x 2 r² 

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 = 5.8 cm

radius of the base = 2.1 cm

Hence, total surface area of the article = 2 ( (2.1) (5.8 + 2 (2.1))

= 2 x 6.6 (10) = 132 cm² 

Therefore, the surface area of the remaining solid is 132 cm².

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