A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical- shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Question

Philoid · Accepted Answer

Let the required bottles = n

Internal diameter of the hemispherical sphere = 30 cm

Internal Radius of the hemispherical sphere = 15 cm

Diameter of the cylindrical bottle = 5 cm

Radius of the cylindrical bottle = 2.5 cm

Now,

Volume of the hemispherical sphere = πr³

= π × 15 × 15 × 15

= π10 × 15 × 15

= 2,250π cm³

And,

Volume of 1 cylindrical bottle = πr²h = π × 2.5 × 2.5 × 6 = 37.5π cm³

Amount of water in n bottles = Amount of water in bowl

n × 37.5π = 2,250π

n = = 60 bottles

So, 60 numbers of bottles are required to empty the bowl.