question_answer

In Fig. 5, is a decorative block, made up of two solids - a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a diameter of 3.5 cm. Find the total surface area of the block, use \[\left( use\,\,\pi =\frac{22}{7} \right)\]

Answer:

Given/ side of a cube \[=6\text{ }cm\]

and the diameter of hemisphere \[=3.5\text{ }cm\]

Now, total surface area of decorative block = total surface area of cube\[\]surface area of base of hemisphere + CSA of hemisphere

\[={{(6)}^{3}}-\frac{22}{7}\times \frac{3.5}{2}\times \frac{3.5}{2}+2\times \frac{22}{7}\times \frac{3.5}{2}\times \frac{3.2}{2}\]

\[=216-\frac{22\times 7}{16}+\frac{22\times 7}{8}\]

\[=216+\frac{154}{16}\]

\[=225.625\,c{{m}^{2}}\]