Question

The internal and external radii of a hollow hemispherical vessel are 15 cm and 16 cm respectively. The cost of painting 1 cm² of the surface is Rs.7. Find the total cost of painting the vessel all over. (ignore the area of edges)

Answer 1

Answer:

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Answer 2

Answer:

Total cost of painting ≈ 21,164 Rs

Step-by-step explanation:

Curved surface area of Hemisphere

$= 2\pi \: {r}^{2}$

Internal Radius of hollow hemisphere r= 15 cm

Internal Curved surface area of Hemisphere

$= 2 \times \frac{22}{7} \times {(15)}^{2} \\ \\ = 2 \times \frac{22}{7} \times 225 \\ \\ = \frac{9900}{7} \\ \\ = 1414.28 \: {cm}^{2}$

External radius of Hemisphere R=16 cm

External Curved surface area of Hemisphere

$= 2\pi {(r)}^{2} \\ \\ = 2 \times \frac{22}{7} \times ( {16)}^{2} \\ \\ = \frac{44}{7} \times 256 \\ \\ = 1609.14 \: {cm}^{2}$

Total area to be painted( ignoring the area of edges)

Total area to be painted( ignoring the area of edges)= Internal surface area+ External surface area

$= 1414.28 + 1609.14 \\ \\ = 3023.42 \: {cm}^{2}$

The cost of painting 1 cm² of the surface is Rs.7

Total cost of painting = 7× 3023.42

= 21,163.96 Rs

≈ 21,164 Rs

Hope it helps you.