Question

d: volume and capacity
chapter 8 practice

1. if the volume of a cone is 52 m³ and the height is 2 m, find the diameter of the cone. round to the nearest metre.

we know

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We are given $V = 52\ m^{3}$ and $h=2\ m$. Substituting into the formula: $52=\frac{1}{3}\pi r^{2}\times2$.

Step3: Solve for $r^{2}$

First, multiply both sides by $\frac{3}{2}$ to get $r^{2}=\frac{52\times3}{2\pi}=\frac{156}{2\pi}=\frac{78}{\pi}$.

Step4: Solve for $r$

$r=\sqrt{\frac{78}{\pi}}\approx\sqrt{\frac{78}{3.14}}\approx\sqrt{24.84}\approx 5\ m$.

Step5: Find the diameter $d$

Since $d = 2r$, then $d=2\times5 = 10\ m$.

Answer:

$10\ m$