Question

1. water tank planning

a company is designing a conical water tank with a height of 15 meters and a diameter of 10 meters. calculate the volume of the water tank in cubic meters. explain each step of your calculation.

Explanation:

Step1: Find the radius

The diameter $d = 10$ meters. The radius $r=\frac{d}{2}=\frac{10}{2}=5$ meters.

Step2: Recall the formula for the volume of a cone

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step3: Substitute the values of $r$ and $h$

Given $h = 15$ meters and $r = 5$ meters. Substitute into the formula: $V=\frac{1}{3}\pi\times(5)^{2}\times15$.

Step4: Calculate the volume

First, $(5)^{2}=25$. Then, $\frac{1}{3}\times25\times15=\frac{1}{3}\times375 = 125$. So, $V = 125\pi$ cubic meters.

Answer:

$125\pi$ cubic meters