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 $₹12per{m}^2$, what will be the cost of painting all these cones? $(Use\pi =3.14$ and take $\sqrt{1.04}=1.02)$

Answer 1

Given, Radius (r) of the cone
$=\frac{40}{2}=20cm=0.2m$
Height (h) of the cone $=1m$
Slant height ($l$) of the cone
$=\sqrt{h^2+r^2}$
$=\left[\sqrt{(1{)}^2+(0.2{)}^2}\right]m=\left(\sqrt{1.04}\right)m=1.02m$

CSA of each cone $=\pi rl$
$=(3.14\times 0.2\times 1.02)m^2=0.64056m^2$

CSA of $50$ such cones $=(50\times 0.64056)m^2$
$=32.028m^2$

Cost of painting $1m^2\text{area}=₹12$
Cost of painting $32.028m^2\text{area}=₹(32.028\times 12)$
$=₹384.336$
$=₹384.34$ (approximately)
Therefore, it will cost $₹384.34$ to paint $50$ such hollow cones.