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The height of a cylinder is twice the radius of its base.

What expression represents the volume of the cylinder, in cubic units?

A. [tex]$4 \pi x^2$[/tex]
B. [tex]$2 \pi x^3$[/tex]
C. [tex]$\pi x^2 + 2 x$[/tex]
D. [tex]$2 + \pi x^3$[/tex]

Sagot :

GinnyAnsweridn
We need to find the expression that represents the volume of a cylinder, given that the height of the cylinder is twice the radius of its base.

First, let \( r \) represent the radius of the base of the cylinder. According to the problem, the height \( h \) of the cylinder is twice the radius. Therefore, we can write the height as:
[tex]\[ h = 2r \][/tex]

The formula for the volume \( V \) of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]

Substituting \( h = 2r \) into the volume formula, we get:
[tex]\[ V = \pi r^2 (2r) \][/tex]

Simplify the expression by multiplying the terms:
[tex]\[ V = 2 \pi r^3 \][/tex]

Hence, the expression that represents the volume of the cylinder in cubic units is:
[tex]\[ 2 \pi r^3 \][/tex]

Given the options, the one that matches this result is:
[tex]\[ \boxed{2 \pi x^3} \][/tex]
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