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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
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
What is the volume formula of a right cone with base area b and height h?
Volume of a cone: 1/3*pi*radius^2 *height
Is the volume of a cone with a height of 6 centimeters and a radius of 2 centimeters?
1/3 * pi * r2 * h= Volume of cone=1/3 (pi)(4)(6)=24/3 pi=8pi8pi=Volume of cone
The volume of a right circular cone of altitude h and base r?
A right circular cone with altitude h and base r is equal to (1/3)*pi*r2*h. This is one third of the volume of a right cylinder with the same dimensions, and can be written as (1/3)*A*h where A is the area of the base circle.
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
Just tell you the proof that volume of cone is equal to three times the volume of cylinder?
Volume of cylinder = PI r^2 h where r = radius and h= height Volume of Cone = (1/3) PI r^2 h where r=radius and h= height Therefore, the volume of a cone is one-third of the volume of a cylinder.
What is the volume of a cone r equals 6 and h equals 8?
The volume of this cone is 301.6 units3
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 radius of a cone if you have height and volume?
Use the equation for the volume of a cone, replace the known height and volume, and solve the resulting equation for the radius.
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
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 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.
The formula for the volume of a cone is most like the formula for the volume of which figure?
The formula for a pyramid. The volume of a pyramid is (1/3)(B)(h). The volume of a cone is essentially the same: (1/3)(B=πr2)(h)
Formula of a volume of a cone?
Volume of cone = Pi/4 x D2 x H/3 where D = diameter H = vertical height
What is the equation of cone for find its m3?
The formula to calculate the volume of a cone is V = (1/3) * π * r^2 * h, where r is the radius of the base, h is the height of the cone, and π is pi. Plug in the values for r and h to find the volume in cubic meters.
What is the rule to find the height of a right circular cone?
Assuming that you're given the volume, the formula is V = 1/3 * pi * r^2 * h plug in r and V and solve for h
