Question

A hemispherical bowl is made up of brass 0.25 CM thickness. the Inner radius of bowl is 5 cm find the ratio of outer surface area to inner surface area

Answer 1

Solutions :-

Given :
Inner Radius = r = 5 cm
Outer Radius = R = (5 + 0.25) cm = 5.25 cm


Find the ratio of outer surface area to inner surface area :-

Outer Surface / Inner Surface
= 2πR²/2πr²
= R²/r²
= 5.25²/5²
= 27.5625/25
= 275625/25 × 10000
= 275625/250000
= 441/400
= 441 : 400


Hence,
The ratio of outer surface area to inner surface area = 441 : 400

Answer 2

Answer:

The ratio of outer surface area to inner surface area is 441 : 400.

Step-by-step explanation:

It is given that the hemispherical bowl is made of brass of 0.25 cm thickness and the inner radius of the bowl is 5 cm.

We know, Thickness of material + Inner radius = external radius

So,

⇒ External radius ( R ) = 5 cm + 0.25 cm

⇒ External radius ( R ) = 5.25 cm

Outer surface area of the bowl = 2πR^2

Internal surface area of the bowl = 2πr^2

Ratio of outer surface area to internal surface area = 2πR^2 / 2πr^2

  ⇒ R^2 / r^2

  ⇒ ( R / r )^2

  ⇒ ( 5.25 cm / 5 cm )^2

  ⇒ ( 525 / 500 )^2

  ⇒ ( 105 / 100 )^2

  ⇒ ( 21 / 20 )^2

   ⇒ 441 : 400

Therefore the ratio of outer surface area to inner surface area is 441 : 400.