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# 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.

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If you open math book you will find a lot of mathematical questions but
youshould have solve this question.
It is from class 10 rd sharma chapter 16 mensuration .

In this question we have to find the capacity of tent and
the cost of the canvas at Rs 100 per square meter.From 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.

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1. Given,

Diameter of the cylinder = 20 m

So, its radius of the cylinder (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 as the slant height of the Cone, then we know that

L2 = r2 + h22

L2 = 152 + 7.52

L2 = 225 + 56.25

L2 = 281.25

L = 12.5 m

Now,

Volume of the cylinder = Ï€R2h1 = V1

V1 = Ï€(10)2 2.5

V1 = 250 Ï€m3

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

V2 = 1/3 Ã— 22/7 Ã— 102 Ã— 7.5

V2 = 250Ï€ m3

So, the total capacity of the tent = volume of the cylinder + volume of the cone = V1 + V2

V = 250 Ï€ + 250 Ï€

V = 500Ï€ m3

Hence, the total capacity of the tent is 500Ï€ m3

And, the total area of canvas required for the tent is S = 2 Ï€Rh1 + Ï€rL

S = 2(Ï€)(10)(2.5) + Ï€(10)(12.5)

S = 550 m2

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

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