Question

the surface of two hemispheres are in the ratio 66 :121 find the ratio of radius​

Answer 1

Let two hemispheres A and B of radius r and R units. According to the Question and our assumption, The ratio of Total Surface Area of Hemisphere A to Hemispheres B is given as 66 : 121.

We know,

• ⇒ TSA of Hemisphere = 3πr²

So,

• ⇒ TSA of A / TSA of B = 66 / 121
• ⇒ 3πr² / 3πR² = 66 / 121
• ⇒ 3πr² / 3πR² = 6 / 11
• ⇒ r² / R² = 6 / 11
• ⇒ r : R = √6 : √11

• So, If the ratio of total Surface area of two hemispheres is given to be 66 : 121, then the ratio of their radii will be √6 : √11

Some Formulae :-

• Volume of Hemisphere = 2/3 πr³

• Curved Surface Area of Hemisphere = 2πr²

• A Hemisphere is generally half of sphere.