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 $100\ cm^2$.

 Given:

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 $15\ cm$. 

To do:

We have to find the cost of painting the toy at $Rs.\ 7$ per $100\ cm^2$.

Solution:

Diameter of the toy $= 16\ cm$

Radius of the toy $(r) = \frac{16}{2}$

$= 8\ cm$

Height of the conical part $(h) = 15\ cm$

Therefore,

Slant height of the toy $(l)=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(8)^{2}+(15)^{2}}$

$=\sqrt{64+225}$

$=\sqrt{289}$

$=17 \mathrm{~cm}$

Total surface area of the toy $=\pi r l+2 \pi r^{2}$

$=\frac{22}{7} \times 8 \times 17+2 \times \frac{22}{7} \times 8 \times 8$

$=\frac{22}{7} \times 8(17+2 \times 8)$

$=\frac{176}{7} \times 33$

$=\frac{5808}{7} \mathrm{~cm}^{2}$

Rate of painting the surface of the toy $=Rs.\ 7$ per $100 \mathrm{~cm}^{2}$

Total cost of painting $=Rs.\ \frac{5808}{7} \times \frac{7}{100}$

$=Rs.\ \frac{5808}{100}$

$=Rs.\ 58.08$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

25 Views

Kickstart Your Career

Get certified by completing the course

Get Started