The volume of a cone is 3πx³ cubic units and its height is x units. Which expression represents the radius of the cone’s base, in units?
Options:
A) 3x
B) 6x
C) 3πx²
D) 9πx²
Answer (2)
To solve the problem of finding the radius of the cone’s base, we need to use the formula for the volume of a cone, which is given by:
V = 3 1 π r 2 h
where:
V is the volume of the cone,
r is the radius of the base,
h is the height of the cone.
According to the problem, the volume of the cone is 3 π x 3 and the height h is x . Plugging these values into the volume formula, we have:
3 π x 3 = 3 1 π r 2 x
First, we can simplify and solve for r 2 :
Multiply both sides by 3 to eliminate the fraction: 9 π x 3 = π r 2 x
Divide both sides by π x to solve for r 2 : 9 x 2 = r 2
Take the square root of both sides to solve for r : r = 9 x 2 = 3 x
So, the expression for the radius of the cone's base is 3 x . Therefore, the correct option is:
A) 3x
The radius of the cone's base can be found using the volume formula for a cone. After calculations, we conclude that the radius is 3 x . Hence, the correct option is A) 3x.
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