Question

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi =\frac{22}{7}$)

Answer 1

The total surface area of the cube
$=6\times (edge{)}^2=6\times 5\times 5c{m}^2=150c{m}^2$.

Note that the part of the cube where the hemisphere is attached is not included in the surface area.

So, the surface area of the block = TSA of cube - base area of hemisphere + CSA of hemisphere

$=150-\pi r^2+2\pi r^2$

$=(150+\pi r^2)cm$,

$=150c{m}^2+(\frac{22}{7}\times \frac{4.2}{2}\times \frac{4.2}{2})c{m}^2$

$=(150+13.86)c{m}^2$

$=163.86c{m}^2$