A hemisphere can with internal radius of 9 cm is completely filled with water. Someone is requested to fill th

Question

A hemisphere can with internal radius of 9 cm is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of 3 cm and height of 4 cm . The number of bottles to be required to make the can empty is

Accepted Answer

Let us compute the volume of both containers:
1. Volume of the hemisphere can:
Given internal radius

R = 9 cm

.

V_{hemi} = \frac{2}{3} π R^{3} = \frac{2}{3} π (9)^{3} = \frac{2}{3} π \times 729 = 2 \times 243 π = 486 π cm^{3}

2. Volume of one cylindrical bottle:
Given diameter

= 3 cm ⟹ radius r = \frac{3}{2} = 1.5 cm

, and height

h = 4 cm

.

V_{cyl} = π r^{2} h = π (\frac{3}{2})^{2} \times 4 = π \times \frac{9}{4} \times 4 = 9 π cm^{3}

Let

n

be the number of bottles required to hold the total volume of water:

n = \frac{V _{hemi}}{V _{cyl}} = \frac{486 π}{9 π} = 54

A hemisphere can with internal radius of $9 cm$ is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of $3 cm$ and height of $4 cm$ . The number of bottles to be required to make the can empty is

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A hemisphere can with internal radius of 9 cm is completely filled with water. Someone is requested to fill this water in a cylindrical bottle with a diameter of 3 cm and height of 4 cm. The number of bottles to be required to make the can empty is