Question
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 13.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
Solution
Let r cm be the radius and h cm be the height of cylinder, then
r = 3.5 cm
and
h = 10 cm.
Let r1 be the radius of the hemisphere, then r1 = 3.5 cm.
Now,
Total Surface area of the article
= Curved Surface Area of the cylinder + 2 (Curved Surface area of hemisphere)
= 2 π rh + 2(2 π r12)
= 2 π rh + 4 π r 2
= 2 π rh + 4 π r2 [∵ r = r1]
= [2 π r (h + 2r)] cm2
