Question
Download Solution PDFThe inner and outer radii of a hemispherical wooden bowl are 6 cm and 8 cm, respectively. Its entire surface has to be polished and the cost of polishing π cm2 is Rs. 50. How much will it cost to polish the bowl?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Inner radius (r1) = 6 cm
Outer radius (r2) = 8 cm
Cost to polish π cm2 = ₹50
Formula used:
Surface area of hemispherical bowl = Outer curved surface area + Inner curved surface area + Area of circular rim
Outer curved surface area = 2πr22
Inner curved surface area = 2πr12
Area of circular rim = π(r22 - r12)
Total surface area = 2πr22 + 2πr12 + π(r22 - r12)
Calculation:
Total surface area = 2π(8)2 + 2π(6)2 + π[(8)2 - (6)2]
⇒ Total surface area = 2π(64) + 2π(36) + π(64 - 36)
⇒ Total surface area = 128π + 72π + 28π
⇒ Total surface area = 228π cm2
Cost per π cm2 = ₹50
Cost = 228 × ₹50
⇒ Cost = ₹11,400
∴ The cost to polish the bowl is ₹11,400.
Last updated on May 28, 2025
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