Question

A decorative blocks as shown in the given figure is made of a cube and a hemisphere. The edge of the cube is $$10\ cm$$, 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 $$=10\ cm$$
Total surface area of cube $$=6(side)^2$$
$$=6\times 10\times 10$$
$$=600\ cm^2$$
Now, Radius of hemisphere $$=3.5\ cm$$
curved surface area of hemisphere $$=2\pi r^2$$
$$=2\times \dfrac{22}{7}\times 3.5\times 3.5$$
$$=77\ cm^2$$
Base area of hemisphere = Area of circle $$=\pi r^2$$
$$=\dfrac{22}{7}\times 3.5 \times 3.5$$
$$=38.5\ cm^2$$
Therefore,
Total surface area of block = Total surface area of a cube +CSA of the hemisphere - Base area of a hemisphere
$$=600+77-38.5$$
$$=638.5\ cm^2$$
Cost of painting the block of $$1\ cm^2=Rs. 0.50$$
cost of painting the block of $$638.5\ cm^2=Rs. 0.50\times 638.5$$
$$=Rs. 319.25$$.