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Question -

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2



Answer -

Given,

Height of the tent =77 dm

Height of a surmountedcone = 44 dm

Height of theCylindrical Portion = Height of the tent – Height of the surmounted Cone

= 77 – 44

= 33 dm = 3.3 m

And, given diameter ofthe cylinder (d) = 36 m

So, its radius (r) ofthe cylinder = 36/2 = 18 m

Let’s consider L asthe slant height of the cone.

Then, we know that

L2 = r2 +h2

L2 =182 + 3.32

L=324 + 10.89

L2 = 334.89

L = 18.3 m

Thus, slant height ofthe cone (L) = 18.3 m

Now, the CurvedSurface area of the Cylinder (S1) = 2πrh

S1 =2π (184.4) m

And, the CurvedSurface area of the cone (S2) = πrL

S= π× 18 × 18.3 m

So, the total curvedsurface of the tent (S) = S+ S2

S = S1 +S2

S = (2π18 × 4.4)+ (π18 × 18.3)

S = 1533.08 m2

Hence, the totalCurved Surface Area (S) = 1533.08 m2

Next,

The cost of 1 m2 canvas= Rs 3.50

So, 1533.08 m2 ofcanvas will cost = Rs (3.50 x 1533.08)

= Rs 5365.8

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