Question

The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost of painting the vessel all over at 14 paise per cm^2.

Answer 1

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Answer 2

$\huge\mathfrak{Solution:}$

Outer radius of the vessel, R = 14 cm

Inner radius of the vessel, r = 10 cm

Area of the outer surface = (2 × pi × R^2) sq units

= (2 × pi × 14 × 14) cm^2

= (392 × pi) cm^2

Area of the inner surface = (2 × pi × r^2) sq units

= (2 × pi × 10 × 10) cm^2

= (200 × pi) cm^2

Area of the ring at the top = pi × (R^2 - r^2) sq units

= pi × [(14)^2 - (10)^2] cm^2

= pi × (14 + 10) × (14 - 10) cm^2

= (96 × pi) cm^2

Total area to be painted = [(392 × pi) + (200 × pi) + (96 × pi)] cm^2

= (688 × pi) cm^2

Cost of painting = Rs. (688 × pi × 14/100)

= Rs. (688 × 22/7 × 14/100)

= Rs. 302.72

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