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Question
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A company deals in casting and moulding of metal on orders received from its clients. In one such order, company is supposed to make 50 toys in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of hemisphere. If the radius of the base of the cone is 21 cm and height is 28 cm.
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- find the volume of 50 toys:
- fine the ratio of the volume of hemisphere to the volume of cone.
Solution
a. Given, Radius of cone, r = 21 cm
Height of cone, h = 28 cm
Also, Radius of hemisphere, r = 21 cm
Volume of 50 toys = 50 × [Volume of sphere + Volume of cone]
= `50 xx (2/3 πr^3 + 1/3 πr^2h)`
= `50 xx 1/3(2 xx 22/7 xx (21)^3 + 22/7(21)^2 xx 28)`
= `50/3 xx 22/7 xx (21)^2 [2 xx 21 + 28]`
= `(50 xx 22 xx 21 xx 21 xx 70)/(7 xx 3)`
= 50 × 22 × 21 × 70
= 1617000 cm3
Hence, volume of 50 toys is 1617000 cm3
b. `"Volume of hemisphere"/"Volume of cone" = (2/3 πr^3)/(1/3 πr^2h)`
= `(2r)/h`
= `(2 xx 21)/28`
= `21/14 = 3/2`
Hence, the required ratio is 3 : 2.
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