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How can two cylinders have the same surface area but different volume?
Change in height and circumference
If you double the volume of a rectangular prism does its surface area double?
No.
Do figures with the same volume always have the same surface area?
figures with the same volume does not have the same surface area.
What happens to the surface area and volume when the height of a three-dimensional solid is doubled?
The change in the surface area depends on the shape. The volume will double.
Are cylinders cubed?
The volume of cylinders are measured in cubic units.
Is integration a way of calculating the volume of the same function equation with an additional dimension or is it always completely new volume rotated about an axis ie a circle to a sphere?
Geometrically the definite integral from a to b is the area under the curve and the double integral is the volume under the surface. So just taking the integral of a function does not yield the volume of the solid made by rotating it around an axis. An integral is only a solid of revolution if you take an infinite sum of infinitesimally small cylinders that is the disk method or you do the same with shells.
Why should volume measures always be placed on a level surface?
When measuring volumes you should always measure from the bottom of the meniscus - the surface of a volume of liquid always has a slight curve called the 'meniscus'. Since the surface of any still volume of water is not flat (it is always either a convex or concave curve), it should be measured on a level surface at eye level - bend your knees until your eyes are level with the miniscus to measure accurately.
What precaution did you have to take when reading the volume of the liquid at its surface?
be careful always in reading.
Why is it important to maximize the surface area to volume ratio?
It is not always the case. If you are out in the cold with insufficient clothing, the important thing - to prevent hypothermia - is to MINIMISE the surface to volume ratio.
Are two cylinders with the same volume are congruent?
Two cylinders with the same volume are not necessarily congruent. One could have a different diameter and length than the other, and still have the same volume.
What is the volume of a piston engine cylinders?
Displacement
How do you calculate the volume of an engine?
Calculate the volume of a single cylinder and multiply it by the number of cylinders.
