Cylinder A has radius 4 times the radius of cylinder B, and height 4 times the height of cylinder B.
What is the ratio of the volume of cylinder A to the volume of cylinder B?
64:1
the ratio of the two lateral areas is
16:1
Vb = pi*r^2*h.
Va = pi*(4r)^2*4h.
Va/Vb = pi*(4r)^2*4h/pi*r^2*h = 64.
Ah, cylinder ratios! Well, to find the ratio of the volume between cylinder A and cylinder B, let's compare their dimensions. If the radius of cylinder A is 4 times the radius of cylinder B, then we can say the radius of cylinder A is 4r, and the radius of cylinder B is r.
Similarly, if the height of cylinder A is 4 times the height of cylinder B, we can say that the height of cylinder A is 4h, and the height of cylinder B is h.
Now, let's calculate the volumes of the cylinders. The volume of cylinder A is given by π(4r)^2(4h), which simplifies to 16πr^2h.
The volume of cylinder B is given by πr^2h.
So, the ratio of the volume of cylinder A to the volume of cylinder B is (16πr^2h) / (πr^2h).
Now, let's cancel out some terms. The π, r^2, and h in the numerator and denominator cancel each other out.
Finally, we're left with the ratio of 16 to 1.
So, the volume of cylinder A is 16 times the volume of cylinder B. That's quite a growth spurt for cylinder A!
To find the ratio of the volume of cylinder A to the volume of cylinder B, we need to compare their volumes.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Let's assume the radius of cylinder B is r and the height of cylinder B is h.
Given that the radius of cylinder A is 4 times the radius of cylinder B, we can say that the radius of cylinder A is 4r. Similarly, the height of cylinder A is 4 times the height of cylinder B, so the height of cylinder A is 4h.
Now, let's calculate the volumes of the two cylinders:
Volume of cylinder A (VA) = π * (4r)^2 * (4h) = 16πr^2h
Volume of cylinder B (VB) = π * r^2 * h
Now we can find the ratio of the two volumes:
VA / VB = (16πr^2h) / (πr^2h)
Simplifying the expression:
VA / VB = 16
Therefore, the ratio of the volume of cylinder A to the volume of cylinder B is 16:1.