Chapter 12.4, Problem 27HP

To determine

To find: the diameter of each container

Answer to Problem 27HP

The diameter of each cylinder is 2.96 units.

Explanation of Solution

Given:

The volume of water in a cone is 93 cubic units

The height of water level in each cylinder is 4.5 units

Formula used:

The volume V of the cylinder is $V=B\cdot h$

Calculation:

The objective is to find the diameter of each container.

The volume V of the cylinder is given by the formula

  $V=B\cdot h$

where $B=\pi r^2$ is the area of the circle and h is the height the cylinder.

The volume V of the cylinder is

  $\begin{array}{c}V=\pi r^{2}h\\ =\pi r^2\left(4.5\right)\\ =4.5\pi r^2\end{array}$

The volume of three congruent cylinder is

  $\begin{array}{c}3V=3\left(4.5\right)\pi r^2\\ =13.5\pi r^2\end{array}$

Since the volume of water is 93 cubic units, so

  $\begin{array}{c}3V=93\\ 13.5\pi r^2=93\\ 135\left(3.14\right)r^2\approx 93\left[Since\pi \approx 3.14\right]\\ 42.39r^2\approx 93\\ r^2=\frac{93}{42.39}\left[Dividebothsidesby42.39\right]\\ \approx 2.19\\ r=\sqrt{2.19}\\ \approx 1.48\end{array}$

Therefore, the diameter of each cylinder is approximately 2(1.48) units that is 2.96 units.

Conclusion:

Therefore, the diameter of each cylinder is 2.96 units.