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 1

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 (2πr²)

S₂ = 2 x 2π(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.