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When 8 spheres with a diameter of 1mm coalesce to form a single sphere how big will it be?
The volume of a sphere is 4/3 (pi) (R)3 .
The volume of each of the 8 spheres is 4/3 (pi) (0.5)3 .
That's (pi/6) mm3 each and 4pi/3 mm3 all together.
To find the size of the combined sphere, start again
with the volume formula and solve it for the radius:
V = 4/3 pi R3
Multiply each side by 3/4 :
3/4 V = pi R3
Divide each side by pi :
3V/4pi = R3
Take the cube root of each side:
R = the cube root of (3V/4pi)
Up above, we wound up with a volume of 4pi/3 mm3 .
So the radius of our new sphere is
cube root of (3V/4pi) = cube root of (3/4pi x 4pi/3) = cube root of (1) = 1 mm
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Check the answer (and a much easier way in which
the answer could have been found):
-- Volume of a sphere = 4/3 pi R3 .
Notice that the volume is proportional to the cube of the radius,
and therefore also to the cube of the diameter.
-- The volume of the big sphere was 8 times the volume of the little ones.
So the big diameter should be the cube root of 8 times the small diameter.
-- The cube root of 8 is 2.
The small diameter is 1.
The big diameter should be 2 x 1 = 2 .
-- I calculated the big radius as 1.
-- Yay !
What else can I help you with?
Name the different types of spheres?
The different types of spheres are named based on their dimensions: a one-dimensional sphere is called a circle, a two-dimensional sphere is called a "2-sphere" or simply a sphere, and a three-dimensional sphere is called a "3-sphere."
What can you tell about the charge signs on spheres?
Spheres can carry positive, negative, or neutral charges. Like charges repel each other (e.g., two positively charged spheres), while opposite charges attract (e.g., a positively charged sphere to a negatively charged sphere). Inducing a charge on a neutral sphere can polarize it temporarily.
What is the capacitance between two concentric spheres?
The capacitance between two concentric spheres is determined by the radius of the spheres and the permittivity of the material between them. It can be calculated using the formula C 4rr / (r - r), where C is the capacitance, is the permittivity of free space, r is the radius of the inner sphere, and r is the radius of the outer sphere.
If the volume of a sphere decreases by a factor of 27 what happens to its diameter?
The volume of a sphere is 4/3 pi R3, which shows that volume is proportional to the cube of the linear dimension. Alternatively, the linear dimension is proportional to the cube-root of the volume.If volume decreases by a factor of 27, diameter decreases by a factor of (cube-root of 27) = 3. Diameter becomes 1/3rd the original diameter.
What is the difference between conducting and non conducting sphere?
Conducting spheres allow for the flow of electric charge, while non-conducting spheres do not. Conducting spheres can redistribute charge in response to an external electric field, while non-conducting spheres cannot. Conducting spheres are typically made of metals, while non-conducting spheres are typically made of insulating materials.
Consider eight little spheres of mercury each with a diameter of 3 mm When they coalesce to form a single sphere how big will it be?
24
How many 100 mile diameter spheres would it take to blanket a 9000 mile diameter sphere with each sphere touching the 6 nearest spheres?
You cannot blanket a large sphere wit smaller spheres because spheres cannot tessellate. There are always gaps between adjacent spheres and so no blanketing is possible.
When making a snowman with an 18 inch diameter top sphere and a ratio of 1 to 2 to 3 in the diameters of the other spheres what will the diameters of the other spheres be?
If you have an 18 inch diameter sphere on top, you'll have a 36 inch diameter sphere in the middle and a 54 inch diameter sphere on the bottom. 18 x 2 = 36 and 18 x 3 = 54
Consider eight little spheres of mercury each with a diameter of 1mm When they coalesce to form a single sphere how big will it be How does its surface area compare with the total surface area of?
The total volume of the new sphere will be 4 times less than the sum of all eight individual volumes. The total surface area will be about half than the total surface area of all individual balls.
Does a planet have its own diameter?
Kind of. All spheres and circles have a diameter, which is the length of a line passing through the center of the sphere. The only problem is that most planets aren't 100% perfect spheres, so the diameter could be different depending on where you start measuring from.
How many 3 inch diameter spheres does it take to fill a 6 cubic yard volume?
Each sphere has a volume of about 0.0003 cubic yards and 6/0.0003 = 20,000 spheres
What is a line that cuts a circle or a sphere in half called?
a bisecting line ? Diameter ______________ The question needs to be re-thought. Lines do not cut spheres in half, no matter where the line is in the sphere. The simplest thing that can cut a sphere in half would be a plane.
What shape is the earth and moon?
Spherical. They are approximately spheres. The earth is more of an oblate sphere, a squashed sphere - this is due to its spin.
If the diameter of a sphere containing 250 ball closely packed is equal to N times the diameter of a single ball what is the value of N?
The diameter is 48 inches.
What is the radius of an object?
The term 'radius' is almost always applied to spheres and circular objects. It is the distance from the edge of the circle/sphere to the center. Double the radius gives you the diameter, which is the longest chord you will be able to get. In other words, the diameter is the largest distance between any two points in a circle or sphere.
How many edge of sphere?
Spheres have no edges.
What is the diameter of a sphere that has a volume of 4189mm3?
The diameter of this sphere is 20 mm
