Question

A tent is cylindrical upto a height of 4m and conical above it. The
diameter of their bases is 32m and the maximum height of the
tent is 16m. If the width of the canvas available is 8m. Find the
minimum length of the canvas used to make the tent.
(use = 22/7​

Answer 1

we have diameter

we will convert it into radius by dividing by 2, then radius will be 16

32/2 = 16m

height = 16m

cylinder = 2πrh

2*22/7*16*16

answer is 1603.14

Answer 2

Length of the canvas used = 150.72 m

Explanation:

Given,

Cylindrical height = 4 m

Diameter of the bases = 32 m

Height of the tent = 16 m

Width of the canvas = 8 m

Surface area of cylinder = 2πrh

where, π = $\frac{22}{7}$

            r = $\frac{32}{2}$

            h = 4

substitute the values in surface area of cylinder

surface area of cylinder = 2πrh

                                        = 2 × $\frac{22}{7}$ × $\frac{32}{2}$ × 4

                                        = 401.92$m^{2}$

Surface area of cone = πrl

                                   =  $\frac{22}{7}$ × $\frac{32}{8}$ × 16

                                   = 803.84$m^{2}$

Surface area of cylinder + Surface area of cone = 401.92$m^{2}$ + 803.84$m^{2}$

                                                                               = 1205.76$m^{2}$

The minimum length of canvas,

let l be the length of the canvas

l × 8 = 1205.76

l = $\frac{1205.76}{8}$

l = 150.72 m

Length of the canvas used = 150.72 m