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How do you prove that the volume of a sphere is equal to the volume of a cone?
Wiki User
∙ 15y ago
The volume of a cone is 1/3(h)(pi)(r2), where h is the height of the cone, pi is 3.1415 and r is the radius of the circle that forms the bottom.
The volume of sphere is 4/3(pi)(r2) where pi is 3.1415 and r is the radius of the sphere.
The (r2) means radius squared. If you put in the values of r for each and the value of h for the cone and solve the two equations, and the answers are the same, the volumes are the same. We can set the expression for the volume of a cone equal to the expression for the volume of a sphere. If, when we plug in the variables, they are equal, the volumes will be equal. Vcone = Vsphere 1/3 (h) (pi) (rc2) = 4/3 (pi) (rs2)
Wiki User
∙ 15y ago
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How do you figure cubic feet of volume in a cone?
The volume of a cone is exactly equal to one third the volume of a cylinder of equal height and radius. The volume of a cylinder is equal to πr2h, so the volume of a cone is πr2h/3
What is the formula of volume in cone and sphere?
Cone: 1/3 ( pi r squared h). sphere: 4/3 pi r cubed
Show that the volume of cylinder is equal to one third the volume of cone?
It isn't. If the cylinder and the cone have the same height and radius, the cylinder has a larger volume (twice as large). If they do not have the same height and radius you need more information to prove their relative volumes.
Is a cone quadrilateral?
No, it is not.
How do you prove that a cone will fit into a cylinder exactlly 3 times?
If you look at the formulas for volume of a cone and volume of a cylinder you can see that a cone will fit in exactly three times if the height and radius of the cone and cylinder are equivalent. A cone has the equation: (1/3)*pi*(r^2)*h=Volume. And a cylinder has the equation: pi*(r^2)*h=Volume. With h equaling height and r equaling radius, you can see that 3*(Volume of a cone)=Volume of a cylinder. Therefore, the cone would fit in three times if height and radius are equivalent for the two figures.
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.
What is the ratio of the volumes of a sphere and a cone with the base diameter and the altitude of the cone equal to the diameter of the sphere?
The ratio is given as the sphere volume divided by the volume of the cone. The volume of a sphere that satisfies these conditions is 4/3 x pi x r cubed, and the volume for the cone is 2/3 x pi x r cubed, where r is the radius and pi is equal to 3.14. Dividing these two volumes, you find the resulting ratio is 2.
What is the relation between sphere and cone?
The ancient Greek mathematician Archimedes proved that the volume of a sphere is four times that of the cone with base equal to a great circle of the sphere and height the radius of the sphere. Maybe this is what the poser of the question meant.
A cone and sphere have the same volume the radius of the sphere and the base of the cone are 6cm what is the height of the cone?
Start by finding the volume of the sphere. You know it's radius is 6cm. The volume of the sphere with respect to the radius is: v = 4/3πr3 So you can plug that radius in to get the volume: v = 4/3π(6cm)3 v = 4/3π216cm3 v = 288πcm3 We know that the volumes of the sphere and the cone are equal, and that the base radius of the cone is six centimeters. Using those, we can work out the cone's height. The volume of a cone is calculated as: v = πr2h we already have the volume and radius, so we simply have to rearrange that equation and solve for h v = πr2h h = v / πr2 and simply plug in our values: h = (288π cm3) / π(6cm)2 h = 288cm3 / 36cm2 h = 8cm So the height of the cone is eight centimeters
How do you figure cubic feet of volume in a cone?
The volume of a cone is exactly equal to one third the volume of a cylinder of equal height and radius. The volume of a cylinder is equal to πr2h, so the volume of a cone is πr2h/3
What is the formula of volume in cone and sphere?
Cone: 1/3 ( pi r squared h). sphere: 4/3 pi r cubed
Show that the volume of cylinder is equal to one third the volume of cone?
It isn't. If the cylinder and the cone have the same height and radius, the cylinder has a larger volume (twice as large). If they do not have the same height and radius you need more information to prove their relative volumes.
What is relationship between cone and sphere?
Actually seeing the relationship between the volumes of a cone (one-third of a cylinder) and a sphere (two-thirds of a cylinder) is hard to beat. The cylinder is 1/3 the volume of the cone
What are everyday uses for pi?
Some of many examples are:- Finding the circumference of a circle Finding the area of a circle Finding the surface area of a sphere Finding the volume of a sphere Finding the surface area of a cylinder Finding the volume of a cylinder Finding the volume of a cone Finding the surface area of a cone
Which shape has 1 curved face and 1 flat face?
A sphere sliced by a plane; or a cone.
What is the volume of cone?
The volume of a cone is equal to 1/3*(pi)*r^2*h. r=radius pi=3.14 h=height
Is a cone quadrilateral?
No, it is not.
