Question

The volume of a conical tent is 1232 $m^3$ and the area of the base floor is 154 $m^2$. Calculate the:
i) radius of the floor;
ii) height of the tent;
iii) length of the canvas required to cover this conical tent if its width is 2 m [4 MARKS]

Answer 1

Part(i): 1 Mark
Part(ii): 1 Mark
Part(iii): 2 Marks

i) Area of the base $=\pi r^2$
$\Rightarrow 154=\frac{22}{7}\times r^2\Rightarrow r^2=\frac{154\times 7}{22}=49$
$\Rightarrow r=7m$
Hence, the radius of the floor is 7 m

ii) Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$\Rightarrow 1232=\frac{1}{3}\times \frac{22}{7}\times 7^2\times h$
$\Rightarrow h=\frac{1232\times 3\times 7}{22\times 49}=24m$

iii) Slant height, $l=\sqrt{h^2+r^2}=\sqrt{{24}^2+7^2}$
$=\sqrt{576+49}=\sqrt{625}$
$=25m$
Curved surface area $=\pi rlsq.unit$
$=\frac{22}{7}\times 7\times 25=550m$
Length of canvas required $=\frac{550}{2}=275m$
Hence, 275 m of canvas is required.