Question

a wooden toy is in the form of a hemisphere is surmounted by a right circular cone. the diameter of the base is 13 cm and the height is 5cm. find the surface area of the toy
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Answer 1

Given,

Diameter of hemisphere = Diameter of the base of the cone = 13 centimetres

Height of the cone = 5 centimetres

For, calculating the surface area of the toy,we have to calculate the CSA of both the hemisphere and the cone.

Now,

Radius of the hemisphere = 13/2 = 6.5 centimetres

CSA of the hemisphere = 2 × π × (6.5)² = 84.5 π cm²

Slant height of cone = ✓(5)²+(6.5)² = ✓25+84.5 = ✓109.5 = 10.4 cm (approx.)

CSA of cone = π × 6.5 × 10.4 = 67.6 π cm²

So,

Total surface area = (84.5π + 67.6π) = π (84.5+67.6) = π × 152.1 = 22/7 × 152.1 = 22 × 21.7 = 477.4 cm² (approx.)

Hence,the approximate surface area of the toy is 477.4 cm².