Question

a hemispherical dome of a building needs to be painted if the circumference of the base of the Dome is 17.6m find the cost of painting gift given the cost of painting is rupees 5 per 100 cm2​

Answer 1

$\sf{\underline{Given:}}$

Circumference (base of dome) $\sf{= 17.6\:m}$

Let r be the radius of the dome.

$\boxed{\sf{Circumference\:of\:circle\:= 2\pi r}}$

$\implies$ $\sf{17.6 = 2 \times \frac{22}{7} \times r}$

$\implies$ $\sf{44r = 17.6 \times 7}$

$\implies$ $\sf{44r = 123.2}$

$\implies$ $\sf{r = \frac{123.2}{44}}$

$\implies$ $\sf{r = 280 \: cm}$

$\sf{\underline{Now:}}$

$\boxed{\sf{C. S. A.\:of\:the\:hemisphere = 2\pi r ^{2}}}$

$\implies$ $\sf{ 2 \times \frac{22}{7} \times 280 \times 280}$

$\implies$ $\sf{ \frac{3449600}{7}}$

$\implies$ $\sf{ 492800 \: sq \: cm}$

$\sf{\underline{Note:}}$

Cost of painting = Rs. 5 per 100 sq cm

$\sf{\underline{So:}}$

Total cost of painting:

$\implies$ $\sf{ \frac{(492800 \times 5)}{100}}$

$\implies$ $\sf{ Rs.\:24640}$

$\sf{\underline{Therefore:}}$

The cost of painting the dome is $\sf{Rs.\:24,640}$