Question

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

• A. $18cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
• B. $28cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
• C. $38cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
• D. $48cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$

Answer 1

The correct option is B $28cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$

Given, a hollow and close cylinder of diameter $20$ cm and height $35$ cm. width of sheet is 1m and cost of sheet is Rs. $56/m$.
Radius $=$ $\frac{d}{2}$ $=10$ cm
So,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 $=\frac{Areaofsheet}{widthofsheet}=\frac{0.282}{1}=0.28$ m $=28$ cm
Area of metal sheet if $10\%$ is wasted then sheet required $=$ Area of sheet $+$ $10\%$ of sheet
$=2828.57+10\%$ of $2828.57$
$=2828.37+282.8$
$=3111.57{cm}^2$