Question

A tent is in the form of a right circular cylinder, surmounted by a cone. The diameter of the cylinder is $24$ m. The height of the cylindrical portion is $11$ m, while the vertex of the cone is $16$ m above the ground. Find the area of the canvas required for the tent is

• A. $1320m^2$
• B. $3120m^2$
• C. $2130m^2$
• D. $1230m^2$

Answer 1

The correct option is A $1320m^2$

Area of canvas required for the tent $=$ Curved surface area of the cylindrical portion $+$ Curved surface area of the cone
$=\left(\pi \right)rl+2\left(\pi \right)rh$
For cylinder:
Radius (r) of the cylinder $=12$ m
Height(h) of the cylinder $=11$m
Curved surface area of cylinder $=2\pi rh=2\left(\pi \right)\times 12\times 11=264\left(\pi \right)$
For cone:
Height (h) of the cone $=$ Height of the vertex from ground $-$ Height of the cylinder
$=16-11=5$ m
Radius (r) of the cone $=12$m
Slant height of the cone $=l$m
$l^2=r^2+h^2$
$l=\sqrt{r^2+h^2}$
$l=\sqrt{5^2+{12}^2}$ $=13$m
Curved Surface area of cone $=\pi rl=\pi \left(12\right)\left(13\right)=\left(156\pi \right)m^2$
Hence, area of canvas $=(264\pi +156\pi )m^2$
$=\left(420\pi \right)m^2=420\times \frac{22}{7}=1320m^2.$