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A cylindrical cup is 15 centimeters in height. When filled to the very top, it holds 450 cubic centimeters of water. What is the radius of the cup, rounded to the nearest tenth? Explain or show your reasoning.

Sagot :

Answer:

The radius of the cup is 3.1 cm.

Step-by-step explanation:

First, we the volume of a right cylinder is [tex]V = πr^{2} h[/tex].

  • V = volume of the cylinder
  • [tex]π[/tex] = pi
  • r = radius of the cylinder
  • h = height of the cylinder

Now, using the information that was given to us, we can plug what we know into the equation: [tex]450=πr^{2}(15)[/tex].

From here, we simply solve for r by isolating it to find the radius. *Remember, what we do to one side we must do to the other.

  1. Divide both sides by 15 to cancel it out on the right: [tex]30=πr^{2}[/tex]
  2. Divide both sides by pi to cancel it out on the right: [tex]9.549296586=r^{2}[/tex] (do not round until you have your final answer)
  3. Square root both sides to cancel out the exponent on the right: [tex]3.090193616=r[/tex]
  4. Round to the nearest tenth to get [tex]r=3.1[/tex]
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