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Ah, what a lovely question! A cylinder with equal height and diameter is called a right circular cylinder. Just imagine it as a beautiful, symmetrical shape that is perfectly balanced and ready for your artistic touch. Remember, there are no mistakes, just happy little accidents in the world of art and geometry.
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How can you prove that the volume of a sphere is equal to the volume of a cylinder provided their radii are equal and the height of the cylinder is equal to the diameter of the sphere?
I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.
The diameter and the height of a cylinder are equal the volume is 2 meters cubed. what is the height of the cylinder?
d = r/2 = 1.3656 V = pi x (d/2)2 x h h = d/2 and V = 2 (d/2)2 times h = 2/pi 2/pi = 0.636619772
How do you find the lateral area of a cylinder?
The area A is equal to 2πrh, where r is the radius and h is the height.
How do you find the volume of a cilinder?
The volume of a cylinder is determined by the formula: volume = (pi sign) radius(squared) height. Since pi is equal to 3.142, then multiply the radius of the circular part of the cylinder and its height.
What is the volume of a cylinder with a radius equal to 4.4 meters and height equal to 67.8 meters?
Volume = pi*4.42*67.8 = 4123.67965 cubic meters
