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 Rs. $5$ per sq. cm. $[Use\pi =22/7]$

Answer 1

The greatest diameter a hemisphere can have $10cm$.

Total surface area of the solid $=$ Surface area of the cube $+$ CSA of the hemisphere $-$ Area of the base of the hemisphere.

$=6\times (10{)}^2+2\times \frac{22}{7}(5{)}^2-\frac{22}{7}(5{)}^2=600+\frac{22}{7}\times 25=678.57c{m}^2$

$\therefore$ Cost of printing the block at the rate of Rs $5$ per sq. cm

The cost of $678.57$sq cm $=678.57\times 5=3392.85$

Hence, the amount is $Rs3393$