The curved surface area of the cylinder is 1760cm^2and its volume is 12320cm^3 find its height
Curved surface of area:
A = 2 r π ∙ h
Divide both sides by 2 r π
A / 2 r π = h
1760 / 2 r π = h
h = 1760 / 2 r π
h = 880 / r π
Volume of area:
V = r² ∙ π ∙ h
V = r² ∙ π ∙ 880 / r π
V = r ∙ 880
880 r = V
Divide both sides by 880
r = V / 880 = 12320 / 880 = 14 cm
h = 880 / 14 π
h = 2 ∙ 440 / 2 ∙ 7 π
h = 440 / 7 π = 20,00805 cm
Approx.
h = 20 cm
My typo.
Curved surface of cylinder:
A = 2 r π ∙ h
Volume of cylinder:
V = r² ∙ π ∙ h
To find the height of the cylinder, we need to use the given information about the curved surface area (CSA) and volume of the cylinder.
First, let's find the height using the formula for the curved surface area of a cylinder:
CSA = 2πrh
Where CSA is the curved surface area, r is the radius of the base of the cylinder, and h is the height of the cylinder.
Given that the curved surface area (CSA) is 1760 cm^2, we can rearrange the formula to solve for h:
h = CSA / (2πr)
Next, let's find the radius (r) using the formula for the volume of a cylinder:
Volume = πr²h
Given that the volume of the cylinder is 12320 cm^3, we can rearrange the formula to solve for r:
r = √(Volume / (πh))
Now, let's substitute the values we know into the formulas and solve step by step:
1. Find the radius (r):
r = √(12320 / (πh))
2. Substitute the value of r into the formula for height (h):
h = CSA / (2πr)
= 1760 / (2π * √(12320 / (πh)))
= 1760 / (2 * √(12320 / h))
= 1760 / (2 * (√12320 / √h))
= 1760 / (2 * (√12320h / √h))
= 1760 / (2 * √(12320h))
3. Simplify the expression further:
h = 880 / (√(12320h))
To solve for h, we'll need to isolate it on one side of the equation:
Multiply both sides of the equation by the square root of (12320h):
√(12320h) * h = 880
Square both sides of the equation to eliminate the square root:
(12320h) * h = 880^2
12320h^2 = 774400
Finally, divide both sides by 12320 to find h:
h^2 = 774400 / 12320
h^2 = 63
Taking the square root of both sides, we get:
h = √63
h ≈ 7.937 cm
Therefore, the approximate height of the cylinder is 7.937 cm.