Question

A decorative block is shown which is made up of two solids, a cube snd s hemisphere. The base of the block is a cube with edbe 6 cm and the hemisphere fixed on the top has a diameter of 4.2 cm

Answer 1

Given - edge of a cube= 6cm

Tsa of cube = 6 ×(edge)^2

=6×36

= 216cm^2

diameter of a hemisphere=4.2cm

radius= 2.1cm

Tsa of the decorative block = tsa of cube - base of a hemisphere + csa of hemisphere

= 216 - πr^2 + 2πr^2

= 216+πr^2

= 216 + 22/7×2.1×2.1

= 216 +13.86

= 229.86cm^2

Answer 2

Total surface area of the block =

= TSA of the cube + CSA of the hemisphere - Base area of the hemisphere

= $\sf\red{6 {(side)}^{2} + 2\pi {r}^{2} - \pi {r}^{2}}$

= $\sf\red{6 \times ( {5cm)}^{2} + \pi {r}^{2} }$

= $\sf\red{150 {cm}^{2} + \frac{22}{7} \times 2.1 \times 2.1 {cm}^{2}}$

= $\sf\red{(150 + 13.86) {cm}^{2} }$

= $\sf\red{163.86 {cm}^{2}}$