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 100 sq. cm [Use $\pi =3.14$]

Answer 1

Side of the cubical block (a)=10 cm

Since the cube is surmounted by a hemisphere, therefore the side of the cube should be equal to the diameter of the hemisphere.

$\therefore$ Largest Diameter of the hemisphere=10 cm

$\therefore$ Radius of the hemisphere (r)=5 cm

$[\because \text{Radius}=\frac{\text{Diameter}}{2}]$

The total surface area of solid=T.S.A of the cube+C.S.A. of the hemisphere-Inner cross-section area of hemisphere

=$6a^2+2\pi r^2-\pi r^2$

=$6a^2+\pi r^2$

=$6(10{)}^2+3.14(5{)}^2$

$[\because \pi =3.14]$

=600+78.5

=$678.5c{m}^2$

The cost of painting per 100-centimeter square is Rs 5.

Total cost for painting=$\frac{Rs678.5}{100}\times 5$

=Rs 33.92

Hence, the total cost for painting will be Rs 33.92