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A cylindrical can has a volume of 250 cm3 and is 10 cm tall. What is its diameter?

User VBobCat
by
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1 Answer

3 votes

Answer:

Approximately
5.6\; {\rm cm}.

Explanation:

The volume
V of a cylinder of height
h and radius
r is
V = \pi\, r^(2)\, h.

Rearrange this equation to obtain an expression for the radius
r of this cylinder:


\begin{aligned}r^(2) &= (V)/(\pi \, h)\end{aligned}.


\begin{aligned}r &= \sqrt{(V)/(\pi \, h)}\end{aligned}.


For the cylinder in this question, it is given that
V = 250\; {\rm cm^(2)} while
h = 10\; {\rm cm}. The radius of this cylinder would be:


\begin{aligned}r &= \sqrt{(V)/(\pi \, h)} \\ &= \sqrt{\frac{250\; {\rm cm^(3)}}{(\pi)\, (10\; {\rm cm})}} \\ &\approx 2.82\; {\rm cm} \end{aligned}.

The diameter
d of a cylinder is twice the value of radius. Thus, the diameter of this cylinder would be:


\begin{aligned} d &= 2\, r \\ &\approx (2)\, (2.82\; {\rm cm}) \\ &\approx 5.6\; {\rm cm}\end{aligned}.

User Rickdmer
by
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