Suppose Cylinder A has the same height but twice the radius of Cylinder B. What is the ratio of the volume of Cylinder B to Cylinder A?
cylinder1:
height = h
radius = r
volume = pi r^2 h = pi r^2h
cylinder2:
height = h
radius = 2r
volume = pi (2r)^2 h
= 4pi r^2h
or
ratio is 1 : 4
so the volume is 4 times as large
To find the ratio of the volume of Cylinder B to Cylinder A, we need to compare their volumes.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
Let's assume the radius of Cylinder B is r, then the radius of Cylinder A would be 2r (twice the radius of B).
Let's say the height of both cylinders is h.
The volume of Cylinder B is Vb = πr^2h.
The volume of Cylinder A is Va = π(2r)^2h = π(4r^2)h = 4πr^2h.
To determine the ratio of Vb to Va, we divide the volume of Cylinder B by the volume of Cylinder A:
Vb/Va = πr^2h / 4πr^2h.
The π and h cancel out, leaving us with:
Vb/Va = r^2 / 4r^2.
Simplifying the expression:
Vb/Va = 1/4.
Therefore, the ratio of the volume of Cylinder B to Cylinder A is 1:4.
To find the ratio of the volume of Cylinder B to Cylinder A, we need to calculate the volumes of both cylinders and then compare them.
The volume V of a cylinder is given by the formula V = π * r² * h, where r is the radius and h is the height.
Let's assume the radius of Cylinder B is r, and its height is h. Since Cylinder B has half the radius and the same height, the radius of Cylinder A will be 2r, and the height will still be h.
Now, let's calculate the volumes of both cylinders.
The volume of Cylinder B (VB) is given by VB = π * r² * h.
The volume of Cylinder A (VA) is given by VA = π * (2r)² * h.
Simplifying these formulas, we have:
VB = π * r² * h
VA = π * (4r²) * h
Now, divide the volume of Cylinder B by the volume of Cylinder A to get the ratio:
Ratio = VB / VA
Ratio = (π * r² * h) / (π * (4r²) * h)
Simplifying further, the common factors of π and h cancel out:
Ratio = (r²) / [(4r²)]
Ratio = 1 / 4
Therefore, the ratio of the volume of Cylinder B to Cylinder A is 1:4 or 1/4.