2. A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7 cm and its volume is 3/2 of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal (take pie = 3 1/7)
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Radius of cone,r=7cm
Volume of cone =23 volume of the hemisphere
31πr2h=23×32πr3
⇒h=3r=3×7=21cm
Surface area of the toy = curved
Surface area of the cone + curved
Surface area of the hemisphere.
Radius of cone,r=7cm
Height of cone,h=21cm
Slant height =l=r2+h2
=72+212=49+441=490=22.135cm
Curved surface area =πrl
=722×7×22.135=486.99cm2
Radius of hemisphere =7cm
Curved surface area =2πr2
=2×722×7×7=308cm2
Curved surface area of the toy =48
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