How to find the volume of a cube - Math
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What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14
What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14
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Vcube = s3 = (2x)3 = 8x3
Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x3
Vcube = s3 = (2x)3 = 8x3
Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x3
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A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?
A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?
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The density of gold is 
and the density of glass is 
. You have a gold cube that is 
in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?
The density of gold is
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Weight = Density * Volume
Volume of Gold Cube = side3= x3
Weight of Gold = 16 g/cm3 * x3
Weight of Glass = 3/cm3 * side3
Set the weight of the gold equal to the weight of the glass and solve for the side length:
16* x3 = 2 * side3
side3 = 16/2* x3 = 8 x3
Take the cube root of both sides:
side = 2x
Weight = Density * Volume
Volume of Gold Cube = side3= x3
Weight of Gold = 16 g/cm3 * x3
Weight of Glass = 3/cm3 * side3
Set the weight of the gold equal to the weight of the glass and solve for the side length:
16* x3 = 2 * side3
side3 = 16/2* x3 = 8 x3
Take the cube root of both sides:
side = 2x
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What is the sum of the number of vertices, edges, and faces of a cube?
What is the sum of the number of vertices, edges, and faces of a cube?
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Vertices = three planes coming together at a point = 8
Edges = two planes coming together to form a line = 12
Faces = one plane as the surface of the solid = 6
Vertices + Edges + Faces = 8 + 12 + 6 = 26
Vertices = three planes coming together at a point = 8
Edges = two planes coming together to form a line = 12
Faces = one plane as the surface of the solid = 6
Vertices + Edges + Faces = 8 + 12 + 6 = 26
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If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?
If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?
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A cubic volume is 
. Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5. This new volume is 125. Therefore, the ratio of new volume to old volume is 125: 1.
A cubic volume is
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A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?
A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?
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If we let 
represent the length of an edge on the smaller cube, its volume is 
.
The larger cube has edges three times as long, so the length can be represented as 
. The volume is 
, which is 
.
The large cube's volume of 
is 27 times as large as the small cube's volume of 
.
If we let
The larger cube has edges three times as long, so the length can be represented as
The large cube's volume of
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What is the volume of a cube with a side length of 7?
What is the volume of a cube with a side length of 7?
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When searching for the volume of a cube we are looking for the amount of the space enclosed by the cube.
To find this we must know the formula for the volume of a cube which is 
Using this formula we plug in the side length for 
to get 
Cube the side length to arrive at the answer of 
The answer is 
.
When searching for the volume of a cube we are looking for the amount of the space enclosed by the cube.
To find this we must know the formula for the volume of a cube which is
Using this formula we plug in the side length for
Cube the side length to arrive at the answer of
The answer is
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If the volume of a cube is 3375, what is the length of each side?
If the volume of a cube is 3375, what is the length of each side?
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To find this we must know the formula for the volume of a cube which is
We plug the volume into the equation yielding 
Then we take the cube root of both sides giving us 
We now know 
The answer is 
.
To find this we must know the formula for the volume of a cube which is
We plug the volume into the equation yielding
Then we take the cube root of both sides giving us
We now know
The answer is
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A box measures 
. How many dice can fit in this box if the dice are cubes with sides of length 
?
A box measures
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Since the dice are 
on each of their sides, 
of them would measure 
in length when standing face-to-face. This means 
dice will fit along the edge of the box that measures 
.
dice will also fit on the edge of the box measuring 
, but 
will not fit since adding an additional die would bring the length of the dice standing face-to-face up to 
. There are no half-dice to fill the gap, so there is a small empty space on this side.
dice will fit along the side that measures 
.
Treating "dice" as the unit of measurement instead of 
and considering only the volume where the dice will fit, one ends up with a rectangular shape measuring 
dice 
dice 
dice. The volume of this shape is the number of dice that will fit in this area (and thus the box). Find the volume by multiplying all lengths of the shape's sides together:
dice 
dice.
Since the dice are
Treating "dice" as the unit of measurement instead of
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What is the volume, in centimeters, of a rectangular prism with a length of 
, a width of 
, and a height of 
?
What is the volume, in centimeters, of a rectangular prism with a length of
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In order to solve this problem, we need to make sure that the measurements given are in uniform units. In this case, we will use centimeters; therefore, we need to convert the other units of meters and millimeters into centimeters via dimensional analysis.
Solve for the width.
Solve for the height.
Now, solve for volume by using the formula 
.
If you calculated 
, then you did not convert into appropriate units.
In order to solve this problem, we need to make sure that the measurements given are in uniform units. In this case, we will use centimeters; therefore, we need to convert the other units of meters and millimeters into centimeters via dimensional analysis.
Solve for the width.
Solve for the height.
Now, solve for volume by using the formula
If you calculated
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What is the volume of a cube with a diagonal one one of its faces of 
?
What is the volume of a cube with a diagonal one one of its faces of
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A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts the qradilateral into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: 
.
Rearrange an solve for 
.
Now, solve for the volume.
A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts the qradilateral into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse:
Rearrange an solve for
Now, solve for the volume.
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A building is in the shape of a perfect cube, with a side length of 
. What is the building's volume, in cubic meters?
A building is in the shape of a perfect cube, with a side length of
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In order to solve this question, we need to convert miles to meters via dimensional analysis and then solve for the volume of the building.
Now, solve for volume.
In order to solve this question, we need to convert miles to meters via dimensional analysis and then solve for the volume of the building.
Now, solve for volume.
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This figure is a cube with one face having an area of 16 in2.
What is the volume of the cube (in3)?
This figure is a cube with one face having an area of 16 in2.
What is the volume of the cube (in3)?
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The volume of a cube is one side cubed. Because we know that one face has an area of 16 in2, then we know that one side must be the square root of 16 or 4. Thus the volume is 
.
The volume of a cube is one side cubed. Because we know that one face has an area of 16 in2, then we know that one side must be the square root of 16 or 4. Thus the volume is
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A cube has a surface area of 
units squared. What is its volume?
A cube has a surface area of
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Since a cube has 
square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is 
, where 
is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to 
:
units
The volume of a cube is 
, where 
is the length of one of the cube's edges. Substituing the solution to the previous equation for 
in the volume equation gives the volume of the cube:
units cubed
Since a cube has
The volume of a cube is
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A cube has a height of 4 feet. What is the volume of the cube in feet?
A cube has a height of 4 feet. What is the volume of the cube in feet?
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We only have the length of one edge, but that is sufficient for finding the volume. The volume of a cube equals one edge multiplied by itself three times: 
We only have the length of one edge, but that is sufficient for finding the volume. The volume of a cube equals one edge multiplied by itself three times:
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Find the volume of the following cube:
Find the volume of the following cube:
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The formula for the volume of a cube is
,
where 
is the side of the cube.
Plugging in our values, we get:
The formula for the volume of a cube is
where
Plugging in our values, we get:
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A cube has a side length of 
meters. What is the volume of the cube?
A cube has a side length of
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The formula for the volume of a cube is:
Since the length of one side is 
meters, the volume of the cube is:
meters cubed.
The formula for the volume of a cube is:
Since the length of one side is
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If the length of the side of a cube is 
, which expression represents the volume of the cube?
If the length of the side of a cube is
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The formula for the volume of the cube is 
Plugging that into Volume equation, we find 
and 
Thus, the answer is 512x6
The formula for the volume of the cube is
Plugging that into Volume equation, we find
Thus, the answer is 512x6
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The density of gold is and the density of glass is . You have a gold cube that is in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?
The density of gold is
Tap to reveal answer
Weight = Density * Volume
Volume of Gold Cube = side3= x3
Weight of Gold = 16 g/cm3 * x3
Weight of Glass = 3/cm3 * side3
Set the weight of the gold equal to the weight of the glass and solve for the side length:
16* x3 = 2 * side3
side3 = 16/2* x3 = 8 x3
Take the cube root of both sides:
side = 2x
Weight = Density * Volume
Volume of Gold Cube = side3= x3
Weight of Gold = 16 g/cm3 * x3
Weight of Glass = 3/cm3 * side3
Set the weight of the gold equal to the weight of the glass and solve for the side length:
16* x3 = 2 * side3
side3 = 16/2* x3 = 8 x3
Take the cube root of both sides:
side = 2x
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What is the sum of the number of vertices, edges, and faces of a cube?
What is the sum of the number of vertices, edges, and faces of a cube?
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Vertices = three planes coming together at a point = 8
Edges = two planes coming together to form a line = 12
Faces = one plane as the surface of the solid = 6
Vertices + Edges + Faces = 8 + 12 + 6 = 26
Vertices = three planes coming together at a point = 8
Edges = two planes coming together to form a line = 12
Faces = one plane as the surface of the solid = 6
Vertices + Edges + Faces = 8 + 12 + 6 = 26
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