# A Solid is Composed of a Cylinder with Hemispherical Ends. If the Whole 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 . - Mathematics

A solid is composed of a cylinder with hemispherical ends. If the whole 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 .

#### Solution

We have a solid composed of cylinder with hemispherical ends.

Radius of the two curved surfaces(r) = 7 cm

Height of cylinder is h.

Total height of the body(h + 2r) = 104 cm

So, total surface area is given by,

Total surface area = Curved surface area of cylinder +2(Curves surface area of hemisphere)

=2pirh+2(2pir^2)

= 2πr(h+2r)

=2(3.14)(7)(104) cm2

=4571.84 cm2

Change the units of curved surface area as,

Total surface area = 4571.87/100 dm^2

= 45.7184 dm2

Cost of polishing the surface is Rs 10 per dm2.

So total cost,

= Rs(45.7184)(10)

= Rs 457.18

Concept: Concept of Surface Area, Volume, and Capacity
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.2 | Q 14 | Page 61