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]

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 cm<sup>2</sup>`

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.