Question

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

Answer 1

Correct Question:

• A Cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

To Find:

• The surface area of the solid

Solution:

• Surface area of solid = Area of cube + Curved surface area of hemisphere - Base area of hemisphere

Area of cube

Here, a = side = 7 cm.

$Area \: of \: cube \: = \: 6 {a}^{2}$

$= 6(7)^{2}$

$= 6 \times 49$

$= 294 \: cm ^{2}$

Curved surface area of hemisphere

• Diameter of hemisphere = 7 cm

Hence,

$radius \: = r = \frac{diameter}{2} = \frac{7}{2} cm$

$area \: of \: hemisphere \: = 2\pi {r}^{2}$

$= 2 \times \frac{22}{7} \times (\frac{7}{2})^{2}$

$= 2 \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}$

$= 77 \: cm ^{2}$

Now,

• Surface area of solid = Area of cube + Curved surface area of hemisphere - Base area of hemisphere

$= 294 + 77 - \frac{77}{2}$

$= 294 + 77 - 38.5$

$=371 - 38.5$

$= 332.5 \: cm^{2}$

Answer:

• Hence, The surface area of solid = 332.5 cm^2.