Question

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100 cm².

Answer 1

From the figure, 

Radius of the hemisphere = 8 cm 

Height of the cone = 15 cm 

Lateral length of the cone = \(\sqrt{h^2+r^2}\) 

= \(\sqrt{15^2+8^2}\) 

= 17 cm 

Curved surface area of hemisphere = 2πr² 

Curved surface area of the cone = πrl 

Total curved surface area of the toy = 2πr² + πrl 

⇒ Total curved surface area of the toy = 2 × (22/7) × 8² + (22/7) × 8 × 17 

⇒ Total curved surface area of the toy = 829.714 cm² 

Cost of painting the toy at Rs. 7 per 100 cm² 

= \(\frac{829.714}{100}\) x 7

= Rs. 58.08