Question

A tent is cylindrical to a height of $4.8$ m and conical above it. The radius of the base is $4.5m$ and the total height of the tent is $10.8$. Find the approximate area of the canvas required for the tent in square meters.

Answer 1

Given a tent is cylindrical of height $4.8m$ and conical above and

the radius of the base is $4.5m$ and a total height of the tent is $10.8m$

The radius of the conical =radius of cylinder$=4.5m$

The height of conical above = total height of tent-height of cylinder

$=10.8-4.8=6m$

And slant height $=l=$$\sqrt{(4.5{)}^2+(6{)}^2}=\sqrt{20.5+36}=\sqrt{56.25}=7.5m$

Then total canvas required =curved surface area of cone +curved surface area of the cylinder

$=\pi rl+2\pi rh$

$=\pi r(l+2h)$

$=\frac{22}{7}\times 4.5(7.5+2\times 4.8)$

$=\frac{22\times 4.5\times 17.1}{7}=241.85m^3$