Question

a cubical block of side 14 cm is surmounted by a hemisphere of maximum diameter. find the surface area of the solid​

Answer 1

Answer:

A cubical block of side 14 cm is surmounted by a hemisphere.

To find:

What is the greatest diameter the hemisphere can have?

Find the surface area of the solid.

Solution:

From given, we have,

The side of a cubical block = a = 14 cm

⇒ The diameter of the hemisphere surmounted = d = 14 cm

Therefore, the greatest diameter the hemisphere can have is equal to the side of a cubical block.

⇒ The radius = r = d/2 = 14/2 = 7 cm

∴ r = 7 cm

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

⇒ Surface area of the solid = 6a² + 2πr² - πr²

⇒ Surface area of the solid = 6a² + πr²

= 6(14)² + 22/7 × 7²

= 1176 + 22 × 7

= 1176 + 154

= 1330

∴ The surface area of the solid is 1330 sq cm.