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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?
Wiki User
∙ 16y ago
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.
Wiki User
∙ 16y ago
Anonymous
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What is a line segment between two points on the circle or sphere which passes through the center?
A diameter - provided it meets the boundary of the circle or sphere on opposite sides.
What is a volume of a sphere with a a diameter of 6cm?
A sphere with a diameter of 6cm has a volume of 113.1 cm3
If the surface area of a sphere is 48.3 cm2 whats its diameter?
The sphere's diameter is 3.921 cm
What is the diameter of a copper sphere that has the same mass as a 8.00 8.00 8.00 cube of aluminum?
The diameter of the sphere is 19.6 cm.
The area of a sphere is 36 pi what is the diameter of the sphere?
d = 6
What is the height of a sphere with a diameter of 3.8?
A sphere's height will always be the same as its diameter.
What was Archimedes discovery about sphere and cylinder?
He discovered the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4⁄3πr3 for the sphere, and 2πr3 for the cylinder. The surface area is 4πr2 for the sphere, and 6πr2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. The sphere has a volume and surface area two-thirds that of the cylinder. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
How do you find the height of a sphere when you only have the diameter?
I can't really believe you're asking this.What's the difference between height, width or diameter when the object is a sphere?It measures the same all over.The diameter IS the height, and the width, and the depth.
What is the volume of a sphere of of 12 inches diameter 6 inch radius and height of 17?
Your measurements are not those of a sphere. The 12 inches and 6 inches are OK, but if it's a sphere, its height would equal the diameter and be equal to 12 inches. Please repost your question and change either the height or the word, "Sphere".
What is a circumscribed cylinder?
A cylinder with base radius r and height 2r. This cylinder circumscribes a sphere of radius r.
The largest sphere to be curved out of a right circular cylinder of radius 7centimeter and height 14centimeter. Find the volume of the sphere.?
Let the radius of the largest sphere that can be carved out of the cube be r cm.The largest sphere which can be carved out of a cube touches all the faces of the cube.∴ Diameter of the largest sphere = Edge of the cube⇒ 2r = 7 cm∴ Volume of the largest sphere
Canister holds 3 tennis balls the diameter of the balls is the same as the diameter of the cylinder 6 cm how much space in the cylinder is not taken?
Canister holds 3 tennis balls the diameter of the balls is the same as the diameter of the cylinder 6 cm how much space in the cylinder is not taken? Since 3 tennis balls fit in the cylinder, the height of the cylinder is 3 * the diameter of a tennis ball Volume of Sphere = 4/3 * Π radius^3 Volume of Cylinder = height * Π radius^2 The diameter of a tennis ball is 6 cm The radius is 3 cm. Volume of 3 balls = 3* 4/3 * Π * radius^3 Volume of 3 balls = 3* 4/3 * Π * 3^3 Height of Cylinder = 3 * 6 cm = 18 cm Volume of cylinder = 18 * Π * 3^2 Space in the cylinder is not taken = Volume of cylinder - Volume of 3 balls Do the math, you should get 169.6 cc for the space in the cylinder is not taken.
If you had a cylinder a cone and a sphere with a radius of 20 feet and a height of 40 feet which would hold the most water?
the cylinder
How and when do you use pi in school?
Some of its uses and applications are as follows:- Circumference of a circle: 2*pi*radius or diameter*pi Area of a circle: pi*radius2 Volume of a sphere: 4/3*pi*radius3 Surface area of a sphere: 4*pi*radius2 Volume of a cone: 1/3*pi*radius2*height Curved surface area of a cone: pi*radius*slant length Volume of a cylinder: pi*radius2*height Entire surface area of a cylinder: (2*pi*radius2)+(diameter*pi*height) Pi is the value of a circle's circumference divided by its diameter Pi is the 16th letter of the Greek alpabet
How do you find the height of the sphere when you know the height of the cube?
if the cube is inside the sphere you needto do some trigonometry and algebra to find out the height or diameter of the sphere. I have never heard someone ask what the height of the sphere is... i didn't think it existed. im pretty sure you need to know the diameter of the sphere. since you didnt give me any numbers to work with this is going to be a confusing explanation. first, the length of the diameter of the sphere is the same length as the length of one corner of the cube to the opposite diagonal corner of the cube. second, you can find this length by applying pythagoreans theorem (a2+b2=c2). third, since you know the height of the cube you need to find the length of the diagonal of one surface of the cube. you can do this by cutting one ofthe surfaces ofthe cubes into a triangle and using the pyth. theorem and solve for the diagonal. remember this number. now take this number and use the pyth. theorem again with the height of the cube and then ythis is the diameter of the sphere.
What is a line segment between two points on the circle or sphere which passes through the center?
A diameter - provided it meets the boundary of the circle or sphere on opposite sides.
What is the diameter of a sphere that has a volume of 4189mm3?
The diameter of this sphere is 20 mm
