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 $100c{m}^2$

Answer 1

Diameter of toy $=16cm\therefore Radius\left(r\right)=\frac{16}{2}=8cm$
Height iof conical part (h) = 15 cm

$\therefore Slantheight\left(l\right)=\sqrt{r^2+h^2}=\sqrt{(8{)}^2+(15{)}^2}=\sqrt{64+225}=\sqrt{289}=17cm$
$\therefore$ Total surface area of the toy
$=\pi rl+2\pi r^2=\frac{22}{7}\times 8\times 17+2\times \frac{22}{7}\times 8\times 8c{m}^2=\frac{22}{7}\times 8[17+2\times 8]c{m}^2=\frac{176}{7}\times 33c{m}^2=\frac{5808}{7}c{m}^2$
Rate of painting the surface of the toy
$=Rs.7per100c{m}^2\therefore Totalcost=\frac{5808}{7}\times \frac{7}{100}=Rs.\frac{5808}{100}=Rs.58.08$