2 cylinders are proportional. The smaller cylinder has a radius of 4 cm. which is half as large as the radius of the larger cylinder.The volume of the smaller cylinder is 250 cubic cm. What is the approximate volume of the larger cylinder?
volume proportional to scale ratio cubed
250 * 8 = 2000
note, I did not have to work that out but here is why
vol = pi r^2 h
if R = 2 r
and H = 2 h
vol big = pi R^2 H = pi (2r)^2 (2 h) = 8 pi r^2 h
To find the approximate volume of the larger cylinder, we can use the concept of proportionality between the two cylinders. Since the smaller cylinder has a radius that is half as large as the radius of the larger cylinder, we can find the ratio of their volumes.
The ratio of the volumes of two similar objects is equal to the cube of the ratio of their corresponding sides. In this case, the corresponding side is the radius of the cylinders.
Let's denote the radius of the larger cylinder as R.
The ratio of the radii of the two cylinders is:
4 cm / R cm = 1/2
Now, we can set up the proportion to find the value of R:
4 cm / R cm = 1 / 2
To solve for R, cross-multiply the proportion:
2 * 4 cm = R cm * 1
8 cm = R cm
So, the radius of the larger cylinder is 8 cm.
Now that we know the radius of the larger cylinder, we can calculate its volume using the formula for the volume of a cylinder, V = π * r^2 * h, where π is a constant (approximately equal to 3.14159), r is the radius, and h is the height (which is not given).
Since the height of both cylinders is not given, we can assume that they have the same height.
The formula for the volume of a cylinder in terms of its radius is:
V = π * r^2 * h
For the smaller cylinder with a radius of 4 cm and a volume of 250 cubic cm, we can plug in the values and solve for the height:
250 cm^3 = π * (4 cm)^2 * h
Simplifying the equation:
250 cm^3 = 16π cm^2 * h
Divide both sides of the equation by 16π cm^2:
250 cm^3 / (16π cm^2) = h
So, the height of both cylinders is approximately 4.97 cm.
Now, we can calculate the volume of the larger cylinder using its radius and height:
V = π * (8 cm)^2 * 4.97 cm
V ≈ 1005.32 cm^3
Therefore, the approximate volume of the larger cylinder is 1005.32 cubic cm.