A drinking glass has the shape of a straight circular cylinder and its capacity is one liter. If the height of the cup is 10 centimeters, then its radius is:
-
\( \cfrac{100}{ \pi } \)
-
\( \cfrac{1}{ \sqrt{10 \pi} } \)
-
\( \cfrac{1}{10\pi} \)
-
\( 10 \sqrt{\pi} \)
-
\( \cfrac{ 10 \sqrt{\pi} }{ \pi } \)
Try to solve it before checking the answer.
\( \cfrac{ 10 \sqrt{\pi} }{ \pi } \)
According to fundamental geometry, the volume of a cylinder is:
V = \pi r^2 h
\]
On the other hand, the volume of in liter is equals to \( V = 1,000 \, cm^3 \).
We also have that \( h = 10 \, cm \). Hence:
\begin{aligned}
1,000 = \pi r^2 (10)
&\Rightarrow
\pi r^2 = 100
\\[.5em]
&\Rightarrow
r^2 = \frac{100}{\pi}
\\[.5em]
&\Rightarrow
r = \frac{10}{ \sqrt{\pi} }
\\[.5em]
&\hspace{2em}
= \boldsymbol{ \frac{ 10 \sqrt{\pi} }{\pi} }
\end{aligned}
\]