Question

A decorative block as shown in the given figure is made of a cube and a hemisphere. The edge of the cube is 10cm, and the radius of the hemisphere attached on the top is 3.5. Find the cost of painting the block at the rate of 50 paise per sq.cm.

Answer 1

Given that side of a cube = 10cm

Total Surface Area of cube = 6(side)²

= 6 × 10 × 10

= 600cm²

Now, Radius of hemisphere = 3.5cm

Curved Surface Area of hemisphere = 2πr² = 2 x 22/7 x 3.5 x 3.5

= 77cm²

Base area of hemisphere = Area of circle = πr²

= 22/7 x 3.5 x 3.5

= 38.5cm²

Therefore,

Total Surface Area of block = Total Surface area of a cube + CSA of the hemisphere - Base area of a hemisphere

= 600 + 77 – 38.5

= 638.5cm²

Cost of painting the block of 1cm² = Rs 0.50

Cost of painting the block of 638.5cm² = Rs 0.50 × 638.5

= Rs 319.25