Question

A tent is in the form of a cylinder of diameter $4.2m$ and height $4m$, surmounted by a cone of equal base and height $2.8m$. find the cost of canvas for making the tent at ₹ $100$ per sq.m.

• A. Rs 6590
• B. Rs 7590
• C. Rs 8590
• D. Rs 9876

Answer 1

The correct option is B Rs.$\left(7590\right)$

The total surface area of the tent:

$T=2\pi r{h}_1+\pi rl$

Where $\pi =\frac{22}{7};r=2.1m$

$h_1=\text{height of the cylinder}=4m$

$h_2=\text{height of the cone}=2.8m$

$l=\text{slant height of the cone}=\sqrt{(2.8{)}^2+(2.1{)}^2}$
$=\sqrt{7.84+4.41}$
$=\sqrt{12.25}$
$\therefore l=3.5m$

So, $T=(2\times \frac{22}{7}\times 2.1\times 4+\frac{22}{7}\times 2.1\times 3.5)m^2$
$=2\times 3.142\times 8.4+3.142\times 2.1\times 3.5$
$=75.9m^2$

Therefore the cost of canvas for making the tent at ₹ $100$ per sq meter $=75.9\times 100=₹7590.$