Question

How can you find the radius of a cylinder with a height of 10 inches and a height volume of $385i{{n}^{3}}$?

Answer 1

Hint: Now we are given with the height and volume of a cylinder. We know that the volume of a cylinder is given by $\pi {{r}^{2}}h$ . Hence we will substitute the value of $\pi $ and h and then equate it to the given volume. Now we will simplify the equation to find the radius of the cylinder.

Complete step by step solution:
Now we are given with the height and volume of a cylinder.
Now we know that the volume of a cylinder is given by the formula $\pi {{r}^{2}}h$ where r is the radius of cylinder h is the height of the cylinder and $\pi $ is a constant with its value equal to 3.14…
Now we are given with the volume as 385$i{{n}^{3}}$
Hence we have $\pi {{r}^{2}}h=385$
Now we are given that the height of the cylinder is 10. Hence substituting h = 10 in the equation we get,
$\Rightarrow \pi {{r}^{2}}\left( 10 \right)=385$
Now dividing the whole equation by 10 we get,
$\Rightarrow \pi {{r}^{2}}=38.5$
Now again dividing the whole equation by $\pi $ we get,
$\Rightarrow {{r}^{2}}=\dfrac{38.5}{\pi }$
Now let us substitute the value of $\pi $ Hence we get,
$\Rightarrow {{r}^{2}}=\dfrac{38.5}{3.14}$
Now multiplying the numerator and denominator by 100 we get,
$\Rightarrow {{r}^{2}}=\dfrac{3850}{314}$
Now taking square root on both sides we get,
$\begin{align}
  & \Rightarrow r=\sqrt{\dfrac{3850}{314}} \\
 & \Rightarrow r=\sqrt{12.26} \\
\end{align}$

Note: Now while solving such problems always check the units of all the values. When the values are substituted in formula the units must be the same. Hence if the units are not same then we convert the units to make them same. Also note that for a cylinder we have curved surface = $2\pi rh$ area total surface area = $2\pi rh+4\pi r$ and volume = $\pi {{r}^{2}}h$