Ex 12.1, 3
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Total surface area of toy
= Curved Surface area of hemisphere
+ Curved Surface area of cone
Curved Surface area of hemisphere
Radius of hemisphere = Radius of cone = r = 3.5 cm
Curved surface area of hemisphere = 2𝜋𝑟2
= 2 ×22/7× (3.5)2
= 2 ×22/7× (3.5)2
= 2 ×22/7× 3.5 × 3.5
= 2 × 22 × 0.5 × 3.5
= 77 cm2
Curved surface area of cone
Curved surface area of cone = 𝝅𝒓𝒍
Radius of cone = r = 3.5 cm
Height of cone = Total height of toy – radius of hemisphere
= 15.5 – 3.5
= 12 cm
Now, we find slant height (l)
We know that
l2 = h2 + r2
l2 = (12)2 + (3.5)2
l2 = (12)2 + (7/2)^2
l2 = 144 + 49/4
l2 = (144(4) + 49)/4
l2 = (576 + 49)/4
l2 = 𝟔𝟐𝟓/𝟒
l = √(625/4)
l = √(25^2/2^2 )
l = 𝟐𝟓/𝟐
l = 12.5 cm
Curved surface area of cone = πr𝑙
= 22/7 × 3.5 × 12.5
= 22 × 0.5 × 12.5
= 137.5 cm2
Now,
Total surface area of toy
= Curved Surface Area of hemisphere
+ Curved Surface Area of cone
= 77 + 137.5
= 214.5 cm2
Hence, total surface area of the toy is 214.5 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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