Question

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.

$use \: \pi = 3 \frac{1}{7}$
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Answer 1

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Solution}}}}}}$

Given r = 7cm and

volume of the cone = 3/2 volume of the hemisphere

1/3 πr^2h = 3/2×2/3πr^3

.°. h=3r

=3×7=21cm

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

Cone :

Radius (r) = 7cm

Height (h) =21cm.

slant height (L)= √r^2+h^2

=22.135 cm.

.°. C.S.A.= πrl

= 22/7×7×22.135= 486.990 cm^2

Hemisphere :

Radius (r) = 7cm

C.S.A. = 2πr^2=2×22/7×7×7

=308 cm^2

.°. C.S.A of the toy = 486.990 + 308

☛ 794.990 cm^2