The volume of a cylinder is given by formula V= pi(3.14) r^2h where r is base radius and h is height
a) the height of a cylinder of radius 5cm and volume 500. Cm^3
B) radius of base of a cylinder of volume 300 cm^3 and height 10 cm
Our teacher didn't really start explaining this but wants us to try ourselves, i wAnt to have an idea about these
V = π r^2 h
a) you are given V = 500 , r = 5 ,so you are missing the h
just plug in the values
500 = π (25) h
divide both sides by 25π
500/(25π) = h
h = 20/π or appr 6.37 ( if you use 3.14 or π)
in B , you are missing the value of r
π r^2 (10) = 300
divide by 10
πr^2 = 30
divide by π
r^2 = 30/π
take square root of both sides
r = √(30/π)
you do the button-pushing.
The radius of a cylindrical construction pipe is 2 feet the pipe is 16 feet long what is the volume use the value 3.144 PI and round your answer to the nearest whole number
a) To find the height of the cylinder, we can rearrange the formula V = πr^2h. Given that V = 500 cm^3 and r = 5 cm, we can substitute these values into the formula and solve for h:
500 = π(5^2)h
500 = 25πh
h = 500 / (25π)
h ≈ 20 / π
h ≈ 6.37 cm
Therefore, the height of the cylinder is approximately 6.37 cm.
b) To find the radius of the base of the cylinder, we can rearrange the formula V = πr^2h. Given that V = 300 cm^3 and h = 10 cm, we can substitute these values into the formula and solve for r:
300 = πr^2(10)
300 = 10πr^2
r^2 = 300 / (10π)
r^2 = 30 / π
r ≈ √(30 / π)
r ≈ √(30 / 3.14)
r ≈ √9.55
r ≈ 3.09 cm
Therefore, the radius of the base of the cylinder is approximately 3.09 cm.
To solve these problems, we can use the formula for the volume of a cylinder, which is V = π * r^2 * h, where V represents the volume, r represents the radius of the base, and h represents the height.
a) Finding the height:
Given:
- Radius (r) = 5 cm
- Volume (V) = 500 cm^3
To find the height (h), we can rearrange the formula and solve for h:
V = π * r^2 * h
500 = π * 5^2 * h
500 = 25π * h
Divide both sides of the equation by 25π to isolate h:
h = 500 / (25π)
h ≈ 8 cm (rounded to the nearest whole number)
Therefore, the height of a cylinder with a radius of 5 cm and a volume of 500 cm^3 is approximately 8 cm.
b) Finding the radius:
Given:
- Volume (V) = 300 cm^3
- Height (h) = 10 cm
To find the radius (r), we rearrange the formula and solve for r:
V = π * r^2 * h
300 = π * r^2 * 10
Divide both sides of the equation by 10π to isolate r:
r^2 = 300 / (10π)
r^2 ≈ 9.549 (rounded to three decimal places)
To find the radius (r), we take the square root of both sides of the equation:
r ≈ √(9.549)
r ≈ 3.09 cm (rounded to two decimal places)
Therefore, the radius of a cylinder with a volume of 300 cm^3 and a height of 10 cm is approximately 3.09 cm.