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 $40$cm and height $1$m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. $12$ per $m^2$, what will be the cost of painting all these cones? (Use $\pi =3.14$ and take $\sqrt{1.04}=1.02$)

Answer 1

Curved surface area of cone will be painted$=\pi rl$

$h=1m;radius=\frac{40}{2}=20cm=0.2m$

and let $l$ be the slant height,

$\therefore l^2=h^2+r^2=1^2+{0.2}^2$

$\Rightarrow l=\sqrt{1+0.04}=\sqrt{1}.04=1.02m$ ($\because \sqrt{1}.04=1.02$ is given in the question)

$\Rightarrow$Curved surface area of 1 cone$=\pi rl=(3.14\times 0.2\times 1.02)m^2=0.64046m^2$

$\Rightarrow$ Curved surface area of 50 cones$=50\times 0.64046=32.028m^2$

Cost of painting $1m^2=Rs.12$

$\therefore$ Cost of painting $32.028m^2=(12\times 32.028)=384.336m^2\approx 384.34$

$\therefore$ Cost of painting 50 cones is $Rs.384.84$