I would like to give a question which
i could not solve.Rd sharma class 10
maths exercise-16.2 mensuration.
In this question we have to find the cost of
polishing its surface at the rate of Rs.10 per dm2.
Given that 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.
Given,
Radius of the hemispherical 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 surface area of the cylinder (S1) = 2 πr h
S1= 2 π(7)(90)
S1 = 3960 cm2
Next,
Curved surface area of the two hemisphere (S2) = 2 (2Ï€r2)
S2 = 2 x 2Ï€(7)2
S2 = 616 cm2
Therefore,
The total curved surface area of the solid (S) = Curved surface area of the cylinder + Curved surface area of the two hemispheres
S = S1 + S2
S = 3960 + 616
S = 4576 cm2 = 45.76 dm2
Given that the cost of polishing the 1 dm2 surface of the solid is Rs. 10
So, the cost of polishing the 45.76 dm2 surface of the solid = Rs (10 x 45.76) = Rs. 457.6
Therefore,
The cost of polishing the whole surface of the solid is Rs. 457.60