(Q8).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 π = 3
1
7
 )

21 cm7 cm.

Given r = cm and

Volume of the cone =
3
2
 volume of the hemisphere
1
3
 πr2h =
3
2
 ×
2
3
 × πr3

∴ h = 3r

= × = cm

Surface area of the toy = C.S.A. of the cone + C.S.A. of hemisphere

Cone:

Radius (r) = 7 cm

Height (h) = 21 cm

Slant height l = √(r2 + h2)

= √( 2 + 2)

= √( + )

= √

= cm.

∴ C.S.A. = πrl

=
× × = cm 2

Hemisphere:

Radius (r) = 7 cm

C.S.A. = 2πr2

= ×
× ×

= cm2

C.S.A. of the toy = + = cm 2