Question

A bus stop is barricaded from the remaining part of the road, by using $50$ hollow cones made of recycled cardboard. Each cone has a base diameter of $40cm$ and height $1m$. If the outer side of each of the cones is to be painted and the cost of painting is $Rs12$ per $m^2$, what will be the cost of painting all these cones? (Use $\pi =3.14$ and $\sqrt{1.04}=1.02$)

Answer 1

Radius of the cone, $r=\frac{40}{2}=20cm=0.2m$

Height of the cone, $h=1m$

Let $l$ be the slant height of a cone.

$\therefore l=\sqrt{r^2+h^2}$

$l=\sqrt{{0.2}^2+1^2}$

$l=\sqrt{1+0.04}$

$l=\sqrt{1.04}$

$l=1.02m$

Rate of painting $=12per{m}^2$

Curved surface of $1$ cone $=\pi rl$

$=(3.14\times 0.2\times 1.02)$

$=0.64056m^2$

$\therefore$ Curved surface of such $50$ cones $=(50\times 0.64056)m^2=32.028m^2$

Cost of painting all these cones $=32.028\times 12=Rs384.34$