Problem Solving

If a 10 cm tall aluminum can that is a perfect right circular cylinder contains 250 cm^3 of soda, what is the diameter of the can in centimeters? $$\left(A\right)\ \frac{5}{\sqrt{\pi}}$$ $$\left(B\right)\ \frac{10}{\pi}$$ $$\left(C\right)\ \frac{10}{\sqrt{\pi}}$$ $$\left(D\right)\ 10\pi$$ $$\left(E\right)\ 5\sqrt{\pi}$$ The OA is the option C.

How can I find the diameter of the can? Help!!!

Hi vjesus12.

To solve this PS question we have to remember the formula of the Volume of a Cylinder: $$V=\pi\cdot r^2\cdot h$$ where "r" is the radius of the circle (the base) and "h" is the height of the cylinder.

For this question, we know that h=10cm and V=250cm^3. Hence, we can find the radius "r" and then we will calculate the diameter d=2*r.
Hence, $$V=\pi\cdot r^2\cdot h$$ $$\Rightarrow\ \ 250=\pi\cdot r^2\cdot10$$ $$\Rightarrow\ \ r^2=\frac{25}{\pi}$$ $$\Rightarrow\ \ r=\sqrt{\frac{25}{\pi}}$$ $$\Rightarrow\ \ r=\frac{5}{\sqrt{\pi}}.$$ Now, we caluclate the diameter $$d=2\cdot r$$ $$d=2\cdot\frac{5}{\sqrt{\pi}}cm$$ $$d=\frac{10}{\sqrt{\pi}}cm.$$ Therefore, the correct answer is the option C.

I really hope this explanation may help you.

Regards.