Question

A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, surmounted by a cone of
equal base and height 2.8 m. Find the capacity of the tent and the cost of canvas for making the
tent at Rs.100 per sq. m.

Answer 1

☝figure
we have,
diameter of base of cylinder, d = 4.2 m
Now, radius of base of cylinder , r= 2.1
m
Height of cylinder, h = 4 m
Now, volume of cylinder =
πr
2
h = 227
×2.1×2.1×4 = 55.44
m
3
Now, radius of base of cone, r = 2.1 m
height of cone,
h1
= 2.8 m
Now slant height of cone, l =
r
2
+
h1
2
−
−
−
−
−
−
−
√
=
4.41 +7.84
−
−
−
−
−
−
−
−
−
−
√
=
12.25


−
−
−
−
−
√
= 3.5 m
Now, volume of cone =
1
3
πr
2
h1
= 13
×
22
7
×2.1×2.1×2.8 = 12.936
m
3
So, capacity of tent = volume of cylinder
+ volume of cone = 55.44 + 12.936 =
68.376
m
2
Now, CSA of cylinder = 2πrh = 2×227×2.1×4 = 52.8
m
2
Now, CSA of cone = πrl =
22
7
×2.1×2
.8 = 18.48
m
2
Area of canvas used = 52.8 + 18.48 =
71.28
m
2
Cost of 1
m
2
of canvas = Rs 100
Cost of 71.28
m
2
of canvas = Rs
(100 × 71.28) = Rs 7128