Mensuration-15

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A toy is in the form of a cone mounted on a hemisphere of radius 7 cm.
The total height of the toy is 31 cm. Find the total surface area.

Solution: Radius of the hemisphere = 7 cm

Total height of the toy = 31 cm

Therefore, height of the conical part = 31 - 7 = 24 cm

Slant height of the conical part, l = √(r2 + h2)

= √(72 + 242)

= √(49 + 576) = √625 = 25 cm

Surface area of the conical part = π r l = 22/7 x 7 x 25 = 550 cm2

Surface area of the hemispherical part = 2 π r2 = 2 x 22/7 x 7 x 7

= 308 cm2

Total surface area of the toy = surface area of the conical part + Surface area of the hemispherical part

= 550 + 308 = 858 cm2

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