Question

A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum are 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of the canvas required to make the tent. Assume that the radii of the upper end of the frustum and the base of the surmounted conical portion are equal. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

$h=8m,r=7m,R=13m.$

Slant height of the frustum of cone is given by

$l=\sqrt{h^2+(R-r{)}^2}$

$=\sqrt{8^2+(13-7{)}^2}$

$=\sqrt{64+36}$

$=\sqrt{100}=10m$

The slant height of the cone be $l_1=12m$ (Given)

Area of the canvas required

=Curved surface area of the tent

=Curved surface area of the frustum + Curved surface area of the cone

$=\pi (R+r)l+\pi r{l}_1$

$=[\frac{22}{7}\times (13+7)\times 10+\frac{22}{7}\times 7\times 12]$

$=\frac{22}{7}(200+84)$

$=892.57m^2$