Question

A cuboidal block of side $10cm$ is surmounted by a hemisphere. What is the largest diameter the hemisphere can have? Find the cost of polishing the total surface area of the side so formed at the rate of $5$ per square $cm$.

Answer 1

The greatest diameter the hemisphere can have $10$cm

T.S.A of the solid $=$ surface area of the cube $+$CSA of the hemisphere $-$ area of the base of the hemisphere

$=6\times {10}^2+2\times \frac{22}{7}\times 5\times 5-\frac{22}{7}\times 5\times 5$

$=600+\frac{22}{7}\times 5\times 5$

$=600+78.56=678.57{cm}^2$

$\therefore$ Cost of printing the block at the rate of $Rs5$per $100$ sq.cm is

$100$sq.cm$=5$

$678.57$sq.cm$=\frac{678.57\times 5}{100}=$Rs$33.93$

Hence the amount is Rs.$33.93$