The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units. What is the height of the cylinder? A. 2 units B. 4 units C. 6 units D. 8 units
Mathematics · High School · Thu Feb 04 2021
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Given:
Height of the cylinder = 3 times the radius
Radius = ?
Volume of the right cylinder = 24 pi
Determine the height of the right cylinder.
Formula for the volume of the right cylinder:
V=πr^2h
Solution:
Equate the given values in a representation,
Let x = Radius
3x = height
Substitute the representation of the radius and the height to the formula for the volume of the rectangle.
V=πr^2h
24 π=π(x)^2(3x)
Solve for x.
To start with combine x^2 with 3x.
24 π=π(x)^2(3x)
24π = 3x^3 π
Divide both sides by 3π to cancel out the 3 π on the other side of the equation.
24π/3π = 3x^3π/3π
x^3 = 8
Take the cube root of both sides in order to determine the value of x.
(x^3)^⅓ = (8)^⅓
x = 2
Radius = 2 units
Height = (2)(3)
Height = 6 unit
Final answer:
Height = 6 unit