Question:

In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.

Answer:

Given: For the conical Part,
height ,h = 4 cm, radius , r = 3 cm
For the cylindrical part,
height ,H = 40 cm, radius ,r = 3 cm
For the hemispherical part,
radius ,r = 3 cm
Slant height of cone (l) = √(h2+r2)
= √(42+32) = √(16+9)
= √25 = 5 cm
Curved surface area of hemisphere = 2πr2
= 2×π×32
= 18π cm2
Curved surface area of cylinder = 2πrH
= 2×π×3×40
= 240π cm2
Curved surface area of cone = πrl
= π×3×5
= 15π cm2
Total area of the toy
= Curved surface area of cone + Curved surface area of cylinder + Curved surface area of hemisphere
= 15π + 240π + 18π
= 273 π cm2
Hence total area of the toy is 273π cm2.

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