Question

a circular cylinder with a diameter of 12 cm and a height of 27 cm is filled with water. An aquarium is in the shaoe of a rectangular prism with the dimensions 35 cm 40cm by 42cm. what isvthe maximum number of full cylinders that can be poured into the fish tank without overflowing it?

Answer 1

Given data:

The diameter of cylinder is d=12 cm.

The height of the cylinder is h= 27 cm.

The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).

The volume of the cylinder is,

`\begin{gathered} V^(\prime)=(\pi)/(4)(d)^2h \\ =(\pi)/(4)(12cm)^2(27\text{ cm)} \\ =3053.628cm^3 \end{gathered}`

The volume of the aquarium is,

`\begin{gathered} V=(35\text{ cm)(40 cm)(42 cm)} \\ =58800cm^3 \end{gathered}`

The number of cylinders that can be pour into aquarium is,

`\begin{gathered} n=(V)/(V^(\prime)) \\ =(58800)/(3053.628) \\ =19.25 \end{gathered}`

Thus, the number of cylinders that can be pour into aquarium is 19.25.