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Question

A toy is in the shape of a hemisphere of same base radius. If the volume of the toy is 231 cm2 and it's diameter is 7 cm. find the height of the toy.

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Solution



Given: Volume of toy =231 cm3

Diameter of a hemisphere =7 cm

radius of hemisphere =Dia2=72=3.5 cm

Cone and hemisphere have equal radius.

radius of hemisphere = radius of cone =3.5 cm

Height of hemisphere = radius of hemisphere =3.5 cm


Let H be the height of toy.

H= height of cone + height of hemisphere

H=h+r , ( h= height of cone)

H=h+3.5

Volume of toy = volume of cone + volume of hemisphere

Volume of toy =13πr2h+23πr3

Volume of toy =πr23(h+2r)

231=22×(3.5)27×3(h+2×3.5)

231=22×7×77×2×2×3(h+7) [3.5=72]

231=11×7×11×1×2×3(h+7)

231=776(h+7)

231×677=h+7

18=h+7

187=h

h=11 cm
Height of toy H=h+r

Height of toy =11+3.5=14.5

Height of toy =14.5 cm

Hence, the height of the toy H=14.5 cm


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