Question

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

Answer 1

The side of the Cube is $5cm.$ So, the total surface area of the cube is,

$6a^2$$=6\times 5\times 5$

$=150c{m}^2$

The radius of hemisphere is $\frac{4.2}{2}=2.1cm.$

The base area of hemisphere is,

$\pi r^2=\frac{22}{7}\times 2.1\times 2.1$

$=13.86c{m}^2$

The surface area of the cube considered is,

$150-13.86=136.14c{m}^2$

The curved surface area of hemisphere is,

$2\pi r^2=2\times \frac{22}{7}\times 2.1\times 2.1$

$=27.27c{m}^2$

The total surface area of solid is $136.14+27.72=163.86c{m}^2$