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There is no ratio of the radius of the base cone to the radius of the base of the cylinder. If they are the same and the height of the cones is the same the ratio of the radius of their bases is 1:1 ant the ratio of the heights is 1:1 and the ratio of the volumes (Vcone:Vcyclinder) is (1/3 π r2 h):(πi r2 h) or 1/3

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โˆ™ 2014-01-26 07:40:33
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Q: What is the ratio of the radius of the cylinder to the radius of the cone?
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What is the ratio of the radii of a cone and a cylinder if they have the same volume and height?

Let the cylinder have radius R and height h Let the cone have radius r and same height h Then: Volume cylinder = πr²h Volume cone = ⅓πR²h If the volume are equal: ⅓πR²h = πr²h → ⅓R² = r² → R² = 3r² → R = √3 r → ratio radii cone : cylinder = 1 : √3


How do you find the volume of a cone that fits exactly inside a cylinder?

volume=pi*radius squared*height/3, where radius is the radius of the cylinder (and will be the radius of the base of the cone),and height is the lenth of the cylinder.


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 is the volume of a cone related to the volume of the cylinder with the same radius and height?

The cone has 1/3 of the volume of the cylinder.


How is the volume of a cone and a cylinder related?

The volume of a cone is 1/3 of the volume of a cylinder with the same radius and height


How does the radius of a cone compared to the radius of a cylinder?

In both cases, the radius can be any positive number.


The base area of a cone or cylinder with radius r is B equals?

The base of a cone or cylinder is a circle. It the radius is r then the base area B=Pi(r2)


What is the similarity ratio of a smaller cone with a height of 9 and a radius of 6 and a larger cone with a height of 15 and a radius of 10?

The smaller to the larger is a ratio of 6:10 or 3:5


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.


A cone surmounted by a cylinder surmounted by a hemisphere find its volume hemisphere 6m in height cylinder 7m in height cone 5m in height not given the radius or diameter?

The radius IS given, since height of hemisphere = radius of hemisphere!


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.


Why is the Volume of a cone Pi times Radius times Radius times height?

Actually it isn't. That's the formula for a cylinder. A cone is 1/3 of that value.

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