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Question
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use ππ = 3.14]
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Solution
We have,
the edge of the cubical of the hemisphere = a = 10 cm
Also, the radius of the hemisphere, `r = 10/2 = 5 `cm
Now,
Total surface area of the solid = TSA of cube + CSA of hemisphere - Area of circle
= 6a2 + 2πr2 - πr2
= 6a2 +πr2
=6 × 10 × 10 × 3.14 × 5 × 5
= 600 + 78.5
= 678.5 cm2
"As, the rate of painting the solid`= ₹5 per 100 cm2`
the cost of painting the solid= `678.5xx5/100 ≈ ₹33.82`
hence, the cost of painting the total surface area of the solid is ₹33.92.
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