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A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $4 cm$ and the diameter of the base is $8 cm$ . What is the total surface area of the toy?

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30.2 (3 + 2) c m 2

40.2 (2 + 1) c m 2

50.2 (2 + 2) c m 2

50.2 (2 + 1) c m 2

answer is C.

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Detailed Solution

Given that the height of the cone is

4 cm

and the diameter of the base is

8 cm

.
Radius of the base will be 4cm.
We have the following formulae,
Slant height of cone

(l) = (h) 2 + (r) 2

Curved Surface of Cone

= π r l

Curved Surface of hemisphere

= 2 π (r) 2

The slant height of cone will be,

l = 42 + 42

l = 16 + 16 l = 42

The total Surface Area of the toy will be the sum of the Curved Surface Area of cone and the Curved Surface Area of hemisphere.

= π r l + 2 π (r) 2

= π r (l + 2 r)

= 227 × 4 × (42 + 2 × 4)

= 50.2 (2 + 2) c m 2

Thus, the total surface area of the toy is

50.2 (2 + 2) c m 2

.
Therefore the correct option is 3.

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