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 Rs 5 per 100 sq cm. [Use π = 3.14.]
Length of side of cubical block = a = 10 cm
Since, a cubical block is surmounted by a hemisphere, so, the largest diameter of hemisphere = 10 cm
Since, hemisphere will be touching the sides of cubical block.
Radius of hemisphere = r = Diameter ÷ 2 = 10/2 cm = 5 cm
Surface area of solid = Surface area of cube – Area of circular part of hemisphere + Curved surface area of hemisphere
Total Surface area of solid = 6a2 – πr2 + 2πr2 = 6a2 + πr2
= 6 × 10 × 10 cm2 + 3.14 × 5 × 5 cm2
= 678.5 cm2
Rate of painting = Rs 5/100 cm2
Cost of painting the total surface area of the solid so formed = Total Surface area of solid × Rate of painting
Cost of painting the total surface area of the solid = Rs 5/100 × 678.5
= Rs 33.925