Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre
The internal and external diameters of a hollow hemispherical vessel are and res
The internal and external diameters of a hollow hemispherical vessel are \( 24 \mathrm{cm} \) and \( 25 c m, \) respectively. The cost to paint \( 1 \mathrm{cm}^{2} \) surface is \( R s .0 .05 . \) Find the total cost to paint the vessel all over. (use \( \left.\pi=\frac{22}{7}\right) \)
- A. Rs.2100
- B. \( R s .1867 \)
- C. \( R s .1245 \)
- D. None of the above
Step-by-step solution
The total surface area of the hollow hemispherical vessel includes the outer curved surface (2πR²), inner curved surface (2πr²), and the rim (π(R²−r²)). With R = 12.5 cm, r = 12 cm, and π = 22/7, total area = π(3R² + r²) = (22/7) × (2451/4) = 53922/28 = 1925.7857 cm². Cost = area × Rs 0.05 = Rs 96.29. As this does not match any given option (A: Rs 2100, B: Rs 1867, C: Rs 1245), the correct answer is 'None of the above'.
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