Question

The interior of building is in the form of a right circular cylinder of radius 7m and height 6m, surmounted by a right circular cone of same radius and of vertical angle ${60}^{\circ }$. Find the cost of painting the building from inside at the rate of Rs 30 per $m^2$

Answer 1

In the above figure BC = 7 m, BD = 6 m and $\angle$ACB = ${30}^{\circ }$

In $△$ABC sin ${30}^{\circ }$ = $\frac{BC}{AC}$

$\Rightarrow$ $\frac{1}{2}=\frac{7}{AC}$

$\Rightarrow$ AC = 14

Curved Surface area of cone = $\pi$rl = $\frac{22}{7}$ × 7 × 14

=308

Curved Surface area of Cylinder = 2$\pi$rh

= 2 × $\frac{22}{7}$ × 7 × 6 = 264
Total curved area = 264+308 =572

Total cost of painting = 572 × 30 =17160 rupees.