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Question -

A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of tent and the cost of the canvas at Rs 100 per square meter.



Answer -


Given,

Diameter of thecylinder = 20 m

So, its radius of thecylinder (R) = 10 m

Height of the cylinder(h1) = 2.5 m

Radius of the cone =Radius of the cylinder (r) = 15 m

Height of the Cone (h2)= 7.5 m

Let us consider L asthe slant height of the Cone, then we know that

L2 = r2 +h22

L2 =152 + 7.52

L=225 + 56.25

L2 =281.25

L = 12.5 m

Now,

Volume of the cylinder= πR2h= V1

V=π(10)2.5

V=250 πm3

Volume of the Cone= 1/3 × 22/7 × r2 × h22 = V2

V= 1/3× 22/7 × 102 × 7.5

V=250π m3

So, the total capacityof the tent = volume of the cylinder + volume of the cone = V+V2

V = 250 π + 250 π

V = 500π m3

Hence, the totalcapacity of the tent is 500π m3

And, the total area ofcanvas required for the tent is S = 2 πRh1 + πrL

S = 2(π)(10)(2.5) +π(10)(12.5)

S = 550 m2

Therefore, the totalcost for canvas is (100) (550) = Rs. 55000

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