Question

A metal sheet of breadth $10cm$ is used to make a cone of radius $14cm$ and slant height $20cm$. Then length of sheet if $25\%$ of sheet is wasted is .

• A. $1.99m$
• B. $1.77m$
• C. $1.82m$
• D. $1.54m$

Answer 1

The correct option is A $1.99m$

We know that, TSA of cone $=\pi r(r+l)$

Now, TSA of cone $=\frac{22}{7}\times 14\times (14+20)$
$=\frac{22}{7}\times 14\times 34$
$=1496c{m}^2$

Let, the length of sheet be $L$.
Breadth of the sheet $=10cm$
$\therefore$ Total area of the sheet $=10\times L$

Since, $25\%$ of sheet was wasted to make the cone, therefore, actual surface area of sheet used to make cone,

$\Rightarrow 10L-25\%\times 10L=1496$

$\Rightarrow 10L-\frac{25}{100}\times 10L=1496$

$\Rightarrow 10L-\frac{25}{10}L=1496$

$\Rightarrow \frac{100L-25L}{10}=1496$

$\Rightarrow L=1496\times \frac{10}{75}$

$\Rightarrow L=199.4cm$

$\therefore L=1.99m$