A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius.The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656cm3.Find the height of the toy.Also,find the cost of painting the hemispherical part of the toy at the rate of Rs.10 per cm2.(Take π= 22/7)
Solution:
Given that,
Radius of the hemisphere = 3.5 cm
Volume of the solid wooden toy = 16656cm3
As, Volume of the solid wooden toy = Volume of the cone + Volume of the hemisphere = 16656cm3
13×πr2L+23×πr3=10016
13×π3.52L+23×π3.53=10016
L + 7 = 13
L = 6 cm
Height of the solid wooden toy = Height of the cone + Radius of the hemisphere
= 6 + 3.5
= 9.5 cm
Now, curved surface area of the hemisphere = 2πR2=2π×(3.5)2 = 77 cm2
Cost of painting the hemispherical part of the toy = 10 77 = Rs. 770