Q. 24.4( 42 Votes )

# 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 of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal

Answer :

Given that, The radius of the base(r) of the cone is 7 cm and its volume is of the hemisphere.

∵ circular base of cone is joined with the plane surface of the hemisphere,

⇒ radius of hemisphere = radius of base of cone = 7 cm

Also,vol. of cone = vol. of hemisphere

⇒ h = 3r

⇒h = 3 × 7

⇒h = 21 cm

Also, slant height(l) = √ r^{2} + h^{2}

⇒ l = √ 7^{2} + 21^{2}

⇒ l = √ 490

⇒ l = 22.13

⇒ Slant Height of cone (l) = 22.13 cm

Now, surface area of toy = surface area of cone + surface area of hemisphere

⇒ surface area of toy = πrl + 2πr^{2}

= πr(l + 2r)

= 794.86 cm^{2}

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AP- Mathematics