Question

What length of tarpaulin $3m$ wide will be required to make comical tent of height $8m$ and base radius $6m$? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20cm$ (use $\pi =3.14$)

Answer 1

REF.Image

According to question

To find $\to$ Length (x) of rectangular tarpaulin such

that we could make a come 08

height ( h) = 8 m

Radius (r) = 6 m

Sol $\to$ Surface area of cone +20 cm = Area of rectangle ...(i)

$[\because$ Given in question, 20 cm extra for margin & wastage on stiching]

[Using formula,curved surface area of cone $=\pi r(r+\sqrt{h^2+r^2})]$

$\therefore$ (1) becomes

$\pi r(r+\sqrt{h^2+r^2})+20=3\times x$

$\Rightarrow 6\pi (6+\sqrt{8^2+6^2})+20=3x$

$\Rightarrow 6\pi (6+10)+20=3x$

$\Rightarrow 96\pi +20=3x$

$\Rightarrow \frac{96\pi +20}{3}=x$ [put $\pi =3.17]$

$107.147=x$

$\therefore$ Required length = 107.147 m