Question

ratio of surface area of sphere and total surface area of hemisphere of same radius is A]3:2 B]2:1 C}4:3 D}4:1

Answer 1

✬ Ratio = 4 : 3 ✬

Explanation:

Given:

• Radius of sphere and hemisphere is same.

To Find:

• What is the ratio of surface area of sphere and tsa of area of hemisphere?

Solution: Let the radius be r .

As we know that

★ Surface area of Sphere = 4πr² ★

★ TSA of Hemisphere = 3πr² ★

• Ratio = Surface area of sphere/TSA of hemisphere

$\implies{\rm }$ Ratio = 4πr² : 3πr²

$\implies{\rm }$ Ratio = 4πr²/3πr²

$\implies{\rm }$ Ratio = 4/3

$\implies{\rm }$ Ratio = 4 : 3

Hence, Ratio is 4 : 3 . Option C is correct.

____________________

• Volume of sphere = 4/3πr³

• Curved Surface area of Hemisphere = 2πr²

• TSA of Hemisphere = 3πr²

• Volume of Hemisphere = 2/3πr³

Answer 2

Answer:

the surface area of the sphere is 4πr2 .

And

The surface area of the hemisphere is equal to sum of the “curved” and “flat” areas (the curved area being half the surface area of the sphere, and the flat area of the sphere being equal to the area of a circle with radius r . The total area, then, is equal to 2πr2 + πr2 = 3πr2 .

So ,

surface area of the sphere/surface area of the hemisphere

=>4πr²/3πr². [πr²] cancelled.

=> The ratio is 4:3

Hope this helps you.

Explanation: