Question

A wooden toy in the form of cone surmounted on a hemisphere. The diameter of the base of the cone is $6cm$ and height is $4cm$. Find the cost of painting the toy at the rate of $Rs.5$ per $1000c{m}^2$.

Answer 1

Given,

Diameter $=6cm$

radius of hemisphere$=$radius of cone$r=\frac{6}{2}=3cm$

Height of cone $=4cm$

Curved surface area of cone $=\pi r\ell$

$\ell =\sqrt{r^2+h^2}=\sqrt{3^2+4^2}$

$=\sqrt{9+16}=\sqrt{25}$
$=5cm$
C.S.A of cone$=\pi r\ell$

$=\frac{22}{7}\times 3\times 5$

$=47.14c{m}^2$
C.S.A of hemisphere $=2\pi r^2$

$=2\frac{22}{7}\times 3^2$

$=56.57$

Total Surface Area $=47.14+28.28$

$=103.71c{m}^2$

Given that cost of painting for $1000c{m}^2$ is $Rs.5$

Cost of painting for $1c{m}^2=\frac{5}{1000}=Rs.0.005$

Cost of painting for $103.71c{m}^2=103.71times0.005$

$=Rs.0.518$