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How do you prove that the volume of a sphere is equal to the volume of a cone?
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)
How to get the formula to find radius in spherometer?
Treat the 3D sphere as a 2D circle. The radius for the sphere is the same radius as for the circle. No matter where on the sphere you place a mark, the distance (radius) from the mark to the centre of the sphere will always be the same as the circle.
If volume of a cone with the same height as cylinder the equation for the radius of cone R in terms of the radius of cylinder r is?
1884 cm3
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
What does the radius of a sphere?
The radius of a sphere is equal distance from the center of the sphere to all points within the sphere.
How do you calculate this- a right circular cone is inscribed in a hemisphere so that base of cone coincides with base of hemisphere what is the ratio of the height of cone to radius of hemisphere?
The vertex of the cone would reach the very top of the sphere, so the height of the cone would be the same as the radius of the sphere. Therefore the ratio is 1:1, no calculation is necessary.
How do you calculate this a right circular cone is inscribed in a hemisphere so that base of cone coincides with base of hemisphere what is the ratio of the height of cone to radius of hemisphere?
Suppose the radius of the sphere is R. The base of the cone is the same as the base of the hemisphere so the radius of the base of the cone is also R. The apex of the cone is on the surface of the hemisphere above the centre of the base. That is, it is at the "North pole" position. So the height of the cone is also the radius of the sphere = R. So the ratio is 1.
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
Difference between a sphere and a cone?
A sphere to a cone is the same as a circle is to a triangle but they are both 3 dimensional.
How to get the formula to find radius in spherometer?
Treat the 3D sphere as a 2D circle. The radius for the sphere is the same radius as for the circle. No matter where on the sphere you place a mark, the distance (radius) from the mark to the centre of the sphere will always be the same as the circle.
How do you prove that the volume of a sphere is equal to the volume of a cone?
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)
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.
Is the volume formula universal for all the figures?
No, the volume formula is not universal for all figures. Different shapes and objects have different formulas to calculate their volume based on their unique dimensions and properties. Each shape requires its own specific formula to accurately determine its volume.
What is the side length of a cube that has the same volume of a sphere with the radius of 1?
The side length of a cube that has the same volume of a sphere with the radius of 1 is: 1.61 units.
If volume of a cone with the same height as cylinder the equation for the radius of cone R in terms of the radius of cylinder r is?
1884 cm3
How do you use great circle in a sentence?
A circle on the surface of a sphere that has the same radius as the sphere.
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
