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 π = 3.14.]

Answer 1

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.