Question

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per $m^2$ . (Note that the base of the tent will not be covered with canvas).

Answer 1

Height of Cylinder = h = 2.1 m

Slant Height of Cone =/=2.8 m
Diameter of Cylinder = 4 m

Radius of Cylinder = Radius of Cone = r = 42 = 2 m

Considering that base of the tent will not be covered with canvas:

Surface Area of Tent = Surface of Cylinder + Surface Area of Cone

= 2. $\pi$ .r.h + $\pi$ .r.1

= $\pi$r (2h+1)

=($\frac{22}{7}$ × 2)((2 × 2.1)+2.8)

=($\frac{22}{7}$ × 2)(4.2+2.8)

=($\frac{22}{7}$ × 2) × 7

=44 $m^2$

Cost of canvas of the tent at the rate of Rs.500 per $m^2$ = 44 × 500 =Rs.22000