MATH SOLVE

7 months ago

Q:
# A cylindrical container is used to hold drinking water on the sidelines for a football team. The maximum capacity of the container is 26,460 mL. If the height of the container is 60 cm, what is the radius of the cylinder? (1 mL = 1 cm3) A. 21 cm B. 7.35 cm C. 220.5 cm D. 42 cm

Accepted Solution

A:

To solve this we are going to use the formula for the volume of a cylinder: [tex]V= \pi r^2h[/tex]

where

[tex]V[/tex] is the volume of the cylinder in cube centimeters

[tex]r[/tex] is the radius of the cylinder in centimeters

[tex]h[/tex] is the height of the cylinder in centimeters

We know for the problem that volume of our cylinder is 26,460 mL. Since 1 mL =[tex]1cm^3[/tex], the volume of our cylinder is [tex]26460cm^3[/tex]. We also know for our problem that the height of our cylinder is 60 cm, so [tex]h=60[/tex]. Lets replace those values in our formula and solve for [tex]r[/tex]:

[tex]V= \pi r^2h[/tex]

[tex]26460= \pi r^2(60)[/tex]

[tex]26460=60 \pi r^2[/tex]

[tex]r^2= \frac{26460}{60 \pi } [/tex]

[tex]r^2= \frac{441}{ \pi } [/tex]

[tex]r= \sqrt{ \frac{441}{ \pi } } [/tex]

[tex]r= \frac{21}{ \sqrt{ \pi } } [/tex]

[tex]r=11.8[/tex]

We can conclude that the radius of the football team's cylindrical container is 11.8 cm

where

[tex]V[/tex] is the volume of the cylinder in cube centimeters

[tex]r[/tex] is the radius of the cylinder in centimeters

[tex]h[/tex] is the height of the cylinder in centimeters

We know for the problem that volume of our cylinder is 26,460 mL. Since 1 mL =[tex]1cm^3[/tex], the volume of our cylinder is [tex]26460cm^3[/tex]. We also know for our problem that the height of our cylinder is 60 cm, so [tex]h=60[/tex]. Lets replace those values in our formula and solve for [tex]r[/tex]:

[tex]V= \pi r^2h[/tex]

[tex]26460= \pi r^2(60)[/tex]

[tex]26460=60 \pi r^2[/tex]

[tex]r^2= \frac{26460}{60 \pi } [/tex]

[tex]r^2= \frac{441}{ \pi } [/tex]

[tex]r= \sqrt{ \frac{441}{ \pi } } [/tex]

[tex]r= \frac{21}{ \sqrt{ \pi } } [/tex]

[tex]r=11.8[/tex]

We can conclude that the radius of the football team's cylindrical container is 11.8 cm