Question

A tent consists of a frustum of a cone, surmounded by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounded 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 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

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

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

$=\sqrt{64+36}$

$=\sqrt{100}=10$

Let the slant height of the cone be $l_1=12m$

Area of the canvas required

=Curved surface of the tent

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

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

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

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

$=892.57m^2$