A hemispherical can with an internal radius of 9 cm is completely filled with water. Someone is requested to f

Question

A hemispherical can with an internal radius of 9 cm is completely filled with water. Someone is requested to fill this water into cylindrical bottles, each with a diameter of 3 cm and a height of 4 cm . The number of bottles required to empty the can is:

Accepted Answer

Let the internal radius of the hemispherical can be

R = 9 cm

.
The volume of the hemispherical can is:

V_{can} = \frac{2}{3} π R^{3} = \frac{2}{3} π \times 9^{3} = \frac{2}{3} π \times 729 = 486 π cm^{3}

For each cylindrical bottle:

* Diameter

= 3 cm ⟹

Radius

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

* Height

h = 4 cm

The volume of one cylindrical bottle is:

V_{bottle} = π r^{2} h = π \times (\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:

N = \frac{V _{can}}{V _{bottle}} = \frac{486 π}{9 π} = 54

A hemispherical can with an internal radius of $9 cm$ is completely filled with water. Someone is requested to fill this water into cylindrical bottles, each with a diameter of $3 cm$ and a height of $4 cm$ . The number of bottles required to empty the can is:

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A hemispherical can with an internal radius of 9cm is completely filled with water. Someone is requested to fill this water into cylindrical bottles, each with a diameter of 3cm and a height of 4cm. The number of bottles required to empty the can is: