the volune if a right circular cylinder is 22 cubic what us the volume in cubic cemimters of a rught cubic cylande with twice the radius and half the height
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To find the volume of the right circular cylinder, we can use the formula:
Volume = π * r^2 * h
Given that the volume of the original cylinder is 22 cubic units, we need to find the radius and height of the cylinder to calculate the volume of the larger cylinder.
Since we have 22 cubic units as the volume of the original cylinder, we can write the equation as:
22 = π * r^2 * h
Now, let's calculate the volume of the larger cylinder.
The larger cylinder has twice the radius and half the height of the original cylinder. So, for the larger cylinder:
Radius = 2 * r
Height = 0.5 * h
Using the formula for the volume of a cylinder, we can calculate the volume of the larger cylinder:
Volume (larger cylinder) = π * (2 * r)^2 * (0.5 * h)
Simplifying the equation, we get:
Volume (larger cylinder) = π * 4 * r^2 * 0.5 * h
= π * 2 * r^2 * h
= 2 * (π * r^2 * h)
We already know that the volume of the original cylinder is 22 cubic units. So, the volume of the larger cylinder can be calculated as:
Volume (larger cylinder) = 2 * 22
= 44 cubic units
Therefore, the volume of the larger cylinder is 44 cubic units.
Now, to convert the volume from cubic units to cubic centimeters, we need to know the conversion factor. Since 1 cubic centimeter is equal to 1 cubic unit, the volume of the larger cylinder in cubic centimeters will be the same as the volume in cubic units, which is:
Volume (larger cylinder in cubic centimeters) = 44 cubic centimeters
Hence, the volume of the larger cylinder is 44 cubic centimeters.