Chapter 6.8, Problem 14STP

To determine

To find: the number of cylinders requires to fill the cubic aquarium.

Answer to Problem 14STP

The number of cans is $45$ .

Explanation of Solution

Given:

The dimension of the cube is $15$ inches.

The radius of the cylinder is $2$ inches.

Height of the cylinder is $6$ inches.

  $a=15,r=2\text{ and }h=6.$ .

Concept used:

Mensuration formula:

  $\begin{array}{l}{v}_{\text{cylinder}}=\pi r^{2}h.\\ v_{\text{cube}}=a^3.\\ a^3=n\pi r^{2}h.\end{array}$

Calculation:

The volume of cubic aquarium is ${15}^3=3375$ .

  $v_{can}=\pi r^{2}h=24\pi =75.36$ .

Since, each can is cylindrical and the aquarium is a cube, the number of cans it will take to fill the aquarium by the volume of one can, or $\frac{a^3}{\pi r^{2}h}$ , where $a=15,r=2\text{ and }h=6.$

The $\text{number of can=}\frac{a^3}{\pi r^{2}h}=\frac{3375}{75.36}=44.79\text{cans}$ .

Since, the number of cans cannot be in decimal so, its round off to $45$ cans.

Hence, the number of cans is $45$ .