Question

find the radius, in centimetres, of the cylinder with a height of 2.5 m and a capacity of 7854 l. round to one decimal place. assume the cylinder is open at both ends. we know

Explanation:

Step1: Convert units

First, convert the height to centimeters ($1m = 100cm$), so $h=2.5m = 250cm$. Convert the volume from liters to cubic - centimeters ($1L = 1000cm^{3}$), so $V = 7854L=7854000cm^{3}$.

Step2: Use cylinder volume formula

The volume formula of a cylinder is $V=\pi r^{2}h$. We know $V = 7854000cm^{3}$ and $h = 250cm$. Rearranging the formula for $r^{2}$, we get $r^{2}=\frac{V}{\pi h}$.

Step3: Calculate $r^{2}$

Substitute the values of $V$ and $h$ into the formula for $r^{2}$: $r^{2}=\frac{7854000}{\pi\times250}$.
$r^{2}=\frac{7854000}{250\pi}=\frac{7854000}{250\times3.14159}\approx9999.49$.

Step4: Calculate $r$

Take the square - root of $r^{2}$ to find $r$: $r=\sqrt{r^{2}}\approx\sqrt{9999.49}\approx100.0cm$.

Answer:

$100.0$