Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles , each of diameter 3 cm and height 4 cm. How many bottles are needed to empty the bowl ?

Answer 1

Hint:
When we come to know about 3D shapes such as cuboid, cube, cone, sphere, cylinder,etc we might think about their various surface areas,volume and perimeter. Volume simply means how much space that 3D body can occupy . This is a very simple problem of Volume of 3D shape i.e. Hemi-Sphere.
Volume of Hemi-Sphere = $\dfrac{2}{3}\pi {r^3}$ in cubic units, (r= radius of Hemi-Sphere)
Volume of cylinder = $\pi {r^2}h$ in cubic units (r= radius of cylinder and h is the height of cylinder)

Complete step by step solution:
Given- radius of the hemispherical bowl is 9 cm.
As the bowl is fully filled, volume of water = Volume of Hemi-Sphere = $\dfrac{2}{3}\pi {r^3}$ = $\dfrac{2}{3}\pi {9^3}$=486π cubic cm
Now, dimensions of cylindrical bottle are such that diameter= 3 cm and height = 4 cm,
So, volume of one bottle= $\pi {r^2}h$ = $\pi {(1.5)^2}4$ (as radius is half the diameter) = 9 π cubic cm
Therefore, number of bottles needed to empty the bowl = $\dfrac{{Volume{\text{ }}of{\text{ }}Hemi - Sphere}}{{Volume{\text{ }}of{\text{ one bottle}}}}$ = $\dfrac{{486\pi }}{{9\pi }}$ =54 bottles
Hence, the required answer is 54 bottles.

Note:
Proper care should be taken while conversion of radius to diameter and/or diameter to radius.
(radius is half the diameter)