Question

Circumference of the base of a hemispherical bowl is 126 cm. How many liters of water would fit in the bowl? (Use 1000 cm3 = 1 liter)

Answer 1

Given,

Circumference of the base of a hemispherical bowl is 126 cm.

To find,

The water capacity of the bowl in litres.

Solution,

Let,the radius of the base of the hemispherical bowl = r cm

[Assume, r as a variable to do the further mathematical calculations.]

So,the circumference of the base of that hemispherical bowl = 2πr cm

Now,if we compare the value of the circumference of the given hemispherical bowl that we have calculated and the value of the circumference of the given hemispherical bowl that is given in the question,we will get the following mathematical equation.

2πr = 126

r = 126 × ½ × 1/π

r = 63/π

So,the volume of the hemispherical bowl = 2/3 × π × (r)³ = 2/3 × π × (63/π)³ =2/3 × π × 250047/π³ = 2/3 × 250047/π² = 2/3 × 250047 × 49/484 =  24504606/1452 = 16876.45 cm³

Now,

1000 cm³ = 1 litre

1 cm³ = 1/1000 litre

16876.45 cm³ = 16876.45/1000 = 16.87 litres

Hence,the water capacity of the hemispherical bowl is approximately 16.87 litres.