Question

A military of height $8.25m$ is in the form of a right circular cylinder of base diameter $30m$ and height $5.5m$ surmounted by a right circular cone of same base radius. Find the length of the canvas use in making the tent, if the breadth of the canvas is $1.5m$

• A. $500.26m$
• B. $224.26m$
• C. $824.26m$
• D. None of these

Answer 1

The correct option is C $824.26m$

Let the length of the canvas of width $1.5m$ required be $L.$

Height of the cone $h=8.25-5.5m$

$=2.75m$

Radius of the cone, $r=15m$

Radius of the cylinder, $R=15m$

Slant height of the cone will be,

$l=\sqrt{h^2+r^2}$

$=15.25m$

Surface area of cone $=\pi rl$

$=3.14\times 15\times 15.25$

$=718.3$

Surface area of cylinder $=2\pi rl$

$=2\times 3.14\times 15\times 5.5$

$=518.1$

Surface Area of tent $=718.3+518.1$

$=1236.4m^2$

Area of the canvas used $=$ Surface area of the tent

$L\times 1.5=1236.4$

$L=\frac{1236.4}{1.5}$

$=824.26m$