Question

A solid composed of a cylinder with hemispherical ends. if the whole length of the solid is 108 cm and the diameter of the hemispherical end is 36 cm, find the cost of polishing its surface at the rate of 70 paise per square cm.

Answer 1

☆Answer

• Total Height of solid = 108cm
• The Height of cylinder portion
• h¹ = h-2×r (r = radius of Semicircle)
• h¹ = 108 - 2×18 = 72cm
• Required Area = Curved Surface area of cylinder + 2× (curved surface area of the hemisphere)

$\longrightarrow \: 22 \pi \: rh + 2(2\pi \: r {}^{2} ) \\ \longrightarrow \: 2\pi \: rh + 4\pi \: r \: {}^{2} = 2\pi \: r(h + 2r) \\ \longrightarrow \: 2 \times \frac{22}{7} \times 18(72 + 2 \times 18) {cm}^{2} \\ \sf \: Now \: Cost \: Of \: 1 {cm}^{2} = 70Paise \\ \therefore \: Cost \: Of \: 2 \times \frac{22}{7} \times 18 \times 108 {cm}^{2} \\ = 2 \times \frac{22}{7} \times 18 \times 108 \times 70 \\ \color{lime}= Rs.8553.60$

Hence, The cost is 8553.60