Question

State true or false:

The minimum length in cm and correct to the nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter $20cm$ and height $35cm$. Given that the width of the metal sheet is $1m$, find the cost of the sheet at the rate of $56$ per m. Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.

• A. True
• B. False

Answer 1

The correct option is A True

Radius $=\frac{Diameter}{2}=10$ cm
We have to find total surface area.
Total surface area $=2\pi r(r+h)=2\times \frac{22}{7}\times 10\times (10+35)=2828.57{cm}^2=0.282m^2$
Cost of sheet $=0.282\times 56=Rs.15.8$
Length of sheet= $=\frac{\text{Area of sheet}}{\text{Width of sheet}}=\frac{0.282}{1}=0.28m=28cm$
Area of metal sheet if $10\%$ is wasted then sheet required $=$ Area of sheet $+10\%$ of sheet

$=2828.57+10\%\times 2828.57$
$=2828.37+282.8$
$=3111.57{cm}^2$