Question

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166\(\frac{5}6\) cm³. 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 = \(\frac{22}7\))

Answer 1

Let h be the height of the cone and r be radius of its base 

Now, 

volume of the wooden toy = \(\frac{1}3πr^2h + \frac{2}3πr^3\)

= \(\frac{77}6(h + 7)\)

According to the question, \(\frac{77}6(h + 6)\) = 166\(\frac{5}6\)

⇒ h = 6 cm 

The height of the wooden toy = 6 cm + 3.5 cm 

= 9.5 cm 

Now, 

curved surface area of the hemispherical part = 2πr² 

= 2π × (3.5)² 

= 77 cm² 

Hence 

the cost of painting the hemispherical part of the toy at the rate of Rs.10 per cm² = 77 × 10 

= Rs.770