Question

A cylindrical vessel , without lid, has to be tin coated on its its both sides. If the radius of the base is $70cm$ and it's height is $1.4m$, calculate the cost of tin coating at the rate of $Rs.3.50$ per $1000c{m}^2$.

Answer 1

Given: Radius of base $=70cm$

Height $=1.4m=140cm$

Since there is no lid we should consider the area of the circular base and lateral surface area of the cylinder.

Lateral surface area$=2\times \pi \times r\times h$

Area of base $=\pi \times r^2$

Since the tin is to be coated on both sides the total area to be coated

$=2\times (2\times \pi \times r\times h)+(\pi \times r^2)$

$=2\pi r(2h+r)$

$=2\times \frac{22}{7}\times 70(280+70)$

$=2\times \frac{22}{7}\times 70\times 350$

$=44\times 3500$

$=154000c{m}^2$

Since, the cost of coating tin per $1000c{m}^2=$Rs. $3.5$

Cost for coating tin per $1c{m}^2=Rs.\frac{3.5}{1000}$

Therefore total cost =total area to be coated$\times$cost for coating $1c{m}^2$

$=154000\times \frac{3.5}{1000}$

$=Rs.539$