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Question -

A solid is composed of a cylinder with hemispherical ends. If the complete length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs.10 per dm2.



Answer -

Given,

Radius of thehemispherical end (r) = 7 cm

Height of the solid =(h + 2r) = 104 cm

h + 2r = 104

h = 104 − (2 × 7)

So, h = 90 cm

We know that,

The curved surfacearea of the cylinder (S1) = 2 πr h

S1= 2π(7)(90)

S1 =3960 cm2

Next,

Curved surface area ofthe two hemisphere (S2) = 2 (2πr2)

S2 = 2x 2π(7)2

S2 =616 cm2

Therefore,

The total curvedsurface area of the solid (S) = Curved surface area of the cylinder + Curvedsurface area of the two hemispheres

S = S1 +S2

S = 3960 + 616

S = 4576 cm=45.76 dm2

Given that the cost ofpolishing the 1 dm2 surface of the solid is Rs. 10

So, the cost ofpolishing the 45.76 dmsurface of the solid = Rs (10 x 45.76)= Rs. 457.6

Therefore,

The cost of polishingthe whole surface of the solid is Rs. 457.60

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