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Vol(cube) = length(diameter)^(3)
Volume(sphere) = (4/3) pi* radius^(3)
Now the radius is '1/2 ' the diameter/length , assuming as 'perfect' fit.
So substituting
Vol(cube) = (2radii)^(3) = (2r)^(3)
To find the 'Ullage' unused space, subtract one from the other.
Vol(cube) - Vol(sph).
(2r)^(3) - (4/3 pi*r^(3)
Factor
r^(3) [ 2^(3) - (4/3 pi ]
=>
4r^(3) [ 2 - pi/3]
NB ' pi = 3.141592.....
So all you need is to find the length of one side of the cube and halve it.
So if the cube is 64 units^(3)
Then the side length is the cube root of 64 units^(3) , which is 4units.
Half of this side length is 2 units ( 4/2) , this is the radius(r).
Substituting
Ullage space is 4(2)^(3) [ 2 - 3.14 / 3] ==>
4(8)[ 2 - 1.047...]
32[ 2 - 1.047...]
32[ 0.9529...] == >
30.9438.... units^(3) is the volume of the Ullage space.
What else can I help you with?
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.
A sphere of radius r inside a cube touches each one of the six sides of the cube what is the volume of the cube in terms of r?
2r3, because if you have a radius touching all six sides, you could then double this to get the diameter of the sphere, which would be 2r, then this would be, being a cube, the length of every edge of the cube, which we cube or put to the 3rd power, to find volume.
How do you find volume of a hollow sphere?
The volume of a sphere is calculated with the formula: V = 4/3 π r3 Volume is four thirds pi times the cube of the radius
HOW TO find the volume of a circle?
The area of a circle is 'pi' multiplied by the square of the circle's radius.The volume of a circle is zero.The volume of a sphere is (4/3 pi) multiplied by the cube of the sphere's radius.
How do you find the radius of a sphere when you have the volume?
The volume of a sphere is 4/3 Pi x radius cubed. So given V you multiply the volume by 3/4 and divide by Pi, then take the cube root of that entire quantity and you have the radius.
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
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.
How large is a sphere that has a cubic volume of 020?
To find the diameter of the sphere, you must calculate the cube root of the volume. The cube root of 20 is approximately 2.71. Therefore, the diameter of the sphere is twice this value, which is approximately 5.42 units.
A sphere of radius r inside a cube touches each one of the six sides of the cube what is the volume of the cube in terms of r?
2r3, because if you have a radius touching all six sides, you could then double this to get the diameter of the sphere, which would be 2r, then this would be, being a cube, the length of every edge of the cube, which we cube or put to the 3rd power, to find volume.
Can you use r square to find the volume of sphere inside of r cube?
No. For a volume you must have a cubic function.
How do you find volume of a hollow sphere?
The volume of a sphere is calculated with the formula: V = 4/3 π r3 Volume is four thirds pi times the cube of the radius
HOW TO find the volume of a circle?
The area of a circle is 'pi' multiplied by the square of the circle's radius.The volume of a circle is zero.The volume of a sphere is (4/3 pi) multiplied by the cube of the sphere's radius.
What a volume of space that is empty of matter?
There may not be any such place, but the farther you get from stars (including ours) the less matter you find. Presumably between galaxies you might find very empty space. Such a volume of space is called a 'vacuum'.
Is using a formula a way to find volume?
Yes. Although the formula would depend on the shape (e.g Cube, sphere) cool
How do you find the diameter of a sphere in solution when change in solution volume after addition of sphere is given?
The change in solution volume will be the volume of the sphere. Let's call that V We know that the volume of a sphere is 4/3 Pi x r^3 So the cube root of 3v/4Pi is the radius, double it and you have the diameter. OR Volume of sphere is 1/6 Pixd^3 so 6V/Pi is the diameter cubed. Take the cube root of 6V/Pi and that is the diameter.
How do you find the hidden tower in farie city?
By clicking on the empty space in the castle.
A sphere fits snugly inside a cube with 2.4 m edges what is the approximate volume?
To find the volume of the sphere that fits snugly inside a cube with 2.4 m edges, we first determine the radius of the sphere, which is half the edge length of the cube. Thus, the radius ( r ) is 1.2 m. The volume ( V ) of a sphere is given by the formula ( V = \frac{4}{3} \pi r^3 ). Plugging in the radius, the volume is approximately ( \frac{4}{3} \pi (1.2)^3 \approx 7.24 , \text{m}^3 ).
