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
Deepak BoraNewbie
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
Share
Given data :-
Volume of toy = 231 cm³
Diameter of hemisphere = 7 cm
radius of hemisphere = radius of cone = 3.5 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