Question

The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm²

Answer 1

Internal radius (r) = ${\displaystyle \frac{20}{2}}$ = 10 cm

External radius (R) = ${\displaystyle \frac{28}{2}}$ = 14 cm

T.S.A of a hollow hemisphere

= π (3R² + r²) sq.units

= ${\displaystyle \frac{22}{7}[3\times {14}^2+{10}^2]}$ cm²

= ${\displaystyle \frac{22}{7}[588+100]}$ cm²

= ${\displaystyle \frac{22}{7}\times 688}$ cm²

Cost of painting the vessel

= ${\displaystyle ₹ 0.14\times \frac{22}{7}\times 688}$

= ${\displaystyle ₹\frac{14}{100}\times \frac{22}{7}\times 688}$

= ${\displaystyle ₹ \frac{2\times 22\times 688}{100}}$

= ${\displaystyle ₹ \frac{30272}{100}}$

= ₹ 302.72 

Cost of painting = ₹ 302.72