what are the dimensions of two cylinders where the first cylinder has a greater surface area and the second cylinder has a greater volume?
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let the height be h, and the radius be r
Volume = πr^2h
Surface area = 2πr^2 + 2πrh
volume > SA
πr^2h > 2πr^2 + 2πrh, divide by πr
rh > 2r + 2h
rh - 2h > 2r
h > 2r/(r-2)
if SA > volume
then h < 2r/(r-2)
for both to be true,
h = 2r/(r-2)
To find two cylinders with different characteristics, one with a greater surface area and the other with a greater volume, we need to consider the formulas for surface area and volume of a cylinder.
The surface area of a cylinder can be calculated using the formula:
A = 2πrh + 2πr^2,
where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
On the other hand, the volume of a cylinder is given by:
V = πr^2h.
Now, let's find the dimensions for the two cylinders.
To have a greater surface area for the first cylinder, we can keep the height (h) constant and increase the radius (r). This means that the first cylinder should have a larger radius than the second cylinder.
For the second cylinder to have a greater volume, we can keep the radius (r) constant and increase the height (h). This means that the second cylinder should have a larger height than the first cylinder.
Therefore, we can conclude that the dimensions of the two cylinders can be different in terms of both radius and height. For the first cylinder, increasing the radius will result in a larger surface area, while for the second cylinder, increasing the height will result in a larger volume.