If the radius of this cylinder is doubled, its volume will be
twice as much
four times as much
eight times as much
is it four times as much?
Yes, if the radius of a cylinder is doubled, its volume will be four times as much. To understand why, let's break down the formula for the volume of a cylinder:
Volume = π * r^2 * h
where π is a mathematical constant (approximately equal to 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder.
When the radius is doubled, the new radius becomes 2r. Substituting this new value into the volume formula, we get:
Volume = π * (2r)^2 * h
= π * 4r^2 * h
= 4 * (π * r^2 * h)
As you can see, the expression (π * r^2 * h) represents the original volume of the cylinder. When we double the radius, we multiply this original volume by 4. Therefore, if the radius of the cylinder is doubled, its volume will be four times as much.