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Which is the greater quantity?
(a) The volume of a cube with surface area inches
(b) The volume of a cube with diagonal inches
The cube with the greater sidelength has the greater volume, so we need only calculate and compare sidelengths.
(a) , so the sidelength of the first cube can be found as follows:
inches
(b) by an extension of the Pythagorean Theorem, so the sidelength of the second cube can be found as follows:
Since ,
. The second cube has the greater sidelength and, subsequently, the greater volume. This makes (b) greater.
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Cube 2 has twice the sidelength of Cube 1; Cube 3 has twice the sidelength of Cube 2; Cube 4 has twice the sidelength of Cube 3.
Which is the greater quantity?
(a) The mean of the volumes of Cube 1 and Cube 4
(b) The mean of the volumes of Cube 2 and Cube 3
The sidelengths of Cubes 1, 2, 3, and 4 can be given values , respectively.
Then the volumes of the cubes are as follows:
Cube 1:
Cube 2:
Cube 3:
Cube 4:
In both answer choices ask for a mean, so we can determine which answer (mean) is greater simply by comparing the sums of volumes.
(a) The sum of the volumes of Cubes 1 and 4 is .
(b) The sum of the volumes of Cubes 2 and 3 is .
Regardless of , the sum of the volumes of Cubes 1 and 4 is greater, and therefore, so is their mean.
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What is the volume of a cube on which one face has a diagonal of
?
One of the faces of the cube could be drawn like this:
Notice that this makes a triangle.
This means that we can create a proportion for the sides. On the standard triangle, the non-hypotenuse sides are both , and the hypotenuse is
. This will allow us to make the proportion:
Multiplying both sides by , you get:
Recall that the formula for the volume of a cube is:
Therefore, we can compute the volume using the side found above:
Now, rationalize the denominator:
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What is the volume of a cube with side length
? Round your answer to the nearest hundredth.
This question is relatively straightforward. The equation for the volume of a cube is:
(It is like doing the area of a square, then adding another dimension!)
Now, for our data, we merely need to "plug and chug:"
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One of your holiday gifts is wrapped in a cube-shaped box.
If one of the edges has a length of 6 inches, what is the volume of the box?
One of your holiday gifts is wrapped in a cube-shaped box.
If one of the edges has a length of 6 inches, what is the volume of the box?
Find the volume of a cube via the following:
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Find the volume of a cube with a height of 3in.
To find the volume of a cube, we will use the following formula:
where a is the length of any side of the cube.
Now, we know the height of the cube is 3in. Because it is a cube, all sides (lengths, widths, height) are the same. That is why we can find any length for the formula.
Knowing this, we can substitute into the formula. We get
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If a cube is inches tall, what is its volume?
To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla . Since a cube has equal sides, we can use
for all three values.
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What is the volume of a cube with a side length equal to inches?
The volume of a a cube (or rectangular prism) can be solved using the following equation:
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What is the volume of a cube in which the edge is equal to , and the value of
is:
First, the value of x must be solved for:
Given the edge of the cube is , plugging in the value of x results in
. Thus, the area would be equal to this value cubed, which would result in 62.
Thus, 62 is the correct answer.
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Give the volume of a cube with surface area 240 square inches.
Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or
square inches. Therefore,
, and
.
The volume is the cube of this, or cubic inches.
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A cube has a side length of , what is the volume of the cube?
A cube has a side length of , what is the volume of the cube?
To find the volume of a cube, use the following formula:
Plug in our known side length and solve
Making our answer:
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Give the volume of a cube with surface area 150 square inches.
Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or
square inches. Therefore,
, and
.
The volume is the cube of this, or cubic inches.
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The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is 1.5 meters. Give the volume of the aquarium in liters.
1 cubic meter = 1,000 liters.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
meters.
Cube this sidelength to get the volume:
cubic meters.
To convert this to liters, multiply by 1,000:
liters.
This is not among the given responses.
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The length of a diagonal of one face of a cube is . Give the volume of the cube.
Since a diagonal of a square face of the cube is, each side of each square has length
.
Cube this to get the volume of the cube:
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An aquarium is shaped like a perfect cube; the perimeter of each glass face is meters. If it is filled to the recommended
capacity, then, to the nearest hundred cubic liters, how much water will it contain?
Note:
A perfect cube has square faces; if a face has perimeter meters, then each side of each face measures one fourth of this, or
meters. The volume of the tank is the cube of this, or
cubic meters.
Its capacity in liters is liters.
of this is
liters.
This rounds to liters, the correct response.
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Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?
Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?
To find the volume of a cube, use the following formula:
Where s is the side length.
Plug in what we know to get our answer:
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Find the area of a cube with a length of 5cm.
To find the volume of a cube, we will use the following formula:
where l is the length, w is the width, and h is the height of the cube.
Now, we know the length of the cube is 5cm. Because it is a cube, all sides are equal. Therefore, the width and the height of the cube are also 5cm.
Knowing this, we will substitute into the formula. We get
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Find the volume of a cube with a height of 8in.
To find the volume of a cube, we will use the following formula:
where l is the length, w is the width, and h is the height of the cube.
Now, we know the height of the cube is 8in. Because it is a cube, all sides/lengths are equal. Therefore, the length and width are also 8in.
Knowing this, we can substitute into the formula. We get
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While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's volume.
While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's volume.
To find the volume of a cube, use the following formula:
So our answer is
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You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the volume of your box be?
You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the volume of your box be?
Begin with the formula for volume of a cube:
Where s is our side length and V is our volume.
Now, we need to plug in our side length and solve for V
So, our volume is
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