Question

a cubical block of side 7cm is surmounted by a hemisphere .what is the greatest diameter the hemisphere can have? find the surface area of the solid

Answer 1

the greatest diameter that can a hemisphere have is 7 cm
surface area of solid=320.5

Answer 2

The largest diameter the hemisphere could have is 7cm as the side of cube is 7cm.

Dimensions of hemisphere = r = 3.5cm

Dimensions of cube = l = 7cm

Surface area of solid =

= $\large\sf{( {l } ^{2} - {\pi \: r}^{2} ) + {5l}^{2} + {2\pi \: r}^{2}}$

= $\large\sf{ {l}^{2} - {\pi \: r}^{2} + {5l}^{2} + {2\pi \: r}^{2}}$

= $\large\sf{{6l}^{2} + {\pi \: r}^{2}}$

= $\large\sf{6 \times {(7)}^{2} + \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}}$

= $\large\sf{6 \times 49 + 11 \times \frac{7}{2}}$

= $\large\sf{294 + \frac{77}{2}}$

= $\large\sf{294+38.5}$

= $\large\sf{{332.5cm}^{2}}$