Chapter 12.4, Problem 26HP

To determine

To name: the dimensions of a cone

Answer to Problem 26HP

Radius is 3 units and the height is 5 units

Explanation of Solution

Given:

The volume of the cone is between 45 cubic units and 55 cubic units.

Formula used:

The volume V of a cone is $V=\frac{1}{3}B\cdot h$

Calculation:

Consider a cone whose radius is r and height is h .

The volume V of a cone is given by the formula

  $V=\frac{1}{3}B\cdot h$

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

Thus, the volume is

  $\begin{array}{c}V=\frac{1}{3}B\cdot h\\ =\frac{1}{3}\pi r^{2}h\\ \approx \frac{3.14}{3}{r}^{2}h\left[Since\pi \approx 3.14\right]\\ \approx \left(1.05\right)r^{2}h\end{array}$

Take r = 3 and h = 5

Thus, the volume of the cone is

  $\begin{array}{c}V\approx \left(1.05\right)3^2\cdot 5\\ =\left(1.05\right)9\cdot 5\\ =\left(1.05\right)45\\ =47.25\end{array}$

Therefore, when radius is 3 units and the height is 5 units, the volume is between 45 cubic units and 55 cubic units.

Conclusion:

Therefore, radius is 3 units and the height is 5 units