Question

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius.The radius of hemisphere is $3.5cm$ and the total wood used in the making of toy is 166$\frac{5}{6}c{m}^3$.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 $c{m}^2$.$(Take\pi =22/7)$

Answer 1

Solution:

Given that,

Radius of the hemisphere $=3.5cm$

Volume of the solid wooden toy = 166$\frac{5}{6}c{m}^3$

As,

Volume of the solid wooden toy = Volume of the cone + Volume of the hemisphere = 166$\frac{5}{6}c{m}^3$

Height of the solid wooden toy = Height of the cone + Radius of the hemisphere

$=6+3.5$

$=9.5cm$

Now, curved surface area of the hemisphere = $2\pi R^2=2\pi \times (3.5{)}^2$ = 77 cm²

Cost of painting the hemispherical part of the toy $=10\times 77=Rs.770$