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# A toy is in the shape of a cone mounted on a hemisphere of same base radius. If the volume of the toy is 231 cm³ and its diameter is 7 cm, then find the height of the toy

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This is the important question that question was asked in 2012 cbse board exam. In this question a toy is in the shape of a cone mounted on a hemisphere. Question from RS Aggarwal Chapter Mensuration  Volume and Surface Area of Solid Exercise 17A Page number 786 problem number 15

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1. Given data :-

Volume of toy = 231 cm³

Diameter of hemisphere = 7 cm

Height of hemisphere= radius of hemisphere= 3.5 cm

height of the toy = H

height of the cone = h

∴ H= height of cone+ height of hemisphere

H = h + r

H = h + 3.5

volume of toy = volume of cone + volume of hemisphere

volume of toy

= [1/3]πr²h + [2/3]πr³

= πr²/3(h+2r)

(22/7) × (3.5)² × (1/3) (h+2 × 3.5) = 231

( 22 × 3.5 × 3.5) / 7 (h+7) = 231 × 3

(231 × 3 × 7) / (3.5× 3.5 × 22) = (h+7)

(3×3)/(0.5×0.5×2)=h+7

900 /50 = h+7

18 = h+7

h = 18-7

h = 11 cm

Height of toy = h+r

= 11+3.5

= 14.5

∴ height of the toy = 14.5 cm

Answer wrong in the book refer this

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