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Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Example Question 1 : Cubes. Possible Answers:. Correct answer:. Explanation : The formula for the volume is given by Since we have the volume, we must take the cube root of the volume to find the length of any one side since it is a cube, all of the sides are equal. Plugging in for the volume, we end up with.
Report an Error. Example Question 2 : Cubes. Not enough information is provided to calculate the answer. Explanation : Because this is a cube, it's helpful to remember that the value of the diagonal of one face is the same length for the other five faces.
The problem can be seen in a simplified square convention: The diagonal merely splits a square into two right triangles. Using the rules for triangles: The hypotenuse of the created triangle is , which can be set equal to to solve for , which in this case will give us the length of one of the cube's edges. Example Question 3 : Cubes.
Explanation : The surface area of a cube can be represented as , since a cube has six sides and the surface area of each side is represented by its length multiplied by its width, which for a cube is , since all of its edges are the same length. We can substitute into this equation and then solve for : So, one edge of this cube is in length. Example Question 4 : Cubes. Find the length of the cube to the nearest tenth of a foot.
Explanation : Since the volume of a cube is length times width times height, with every measurement being the same, we just need to take the cube root of the volume:. Rounded to the nearest tenth, the length is 3. Example Question 5 : Cubes. Find the length of one of the cube's sides:.
Explanation : The only information that is given is that the diagonal of one of the faces of the cube is. That means the Pythagorean Theorem for this case can be rewritten as Looking back at the problem, the only information given is the hypotenuse for one of the two triangles. Example Question 6 : Cubes. Explanation : Since cubes have side lengths that are equal and we find the volume by , then the side length of a cube with a volume of is simply. Example Question 7 : Cubes. Explanation : Recall how to find the surface area of a cube: Since the question asks you to find the length of a side of this cube, rearrange the equation.
Substitute in the given surface area to find the side length. Example Question 8 : Cubes. So strictly speaking, the cube has zero volume. When we talk about the volume of a cube, we really are talking about how much liquid it can hold, or how many unit cubes would fit inside it.
Think of it this way: if you took a real, empty metal box and melted it down, you would end up with a small blob of metal. If the box was made of metal with zero thickness, you would get no metal at all. That is what we mean when we say a cube has no volume. The strictly correct way of saying it is "the volume enclosed by a cube" - the amount space there is inside it.
But many textbooks simply say "the volume of a cube" to mean the same thing. So we can take the volume of a cube formula and set it equal to the volume that we actually know: 64 centimeters cubed. So in order to find the length of the edge, which is a side, we need to cube root both sides of this equation.
On the left-hand side, the cube root cancels all the cube. And then the cube root of 64 is four and the cube root of centimeters cubed would be centimeters.
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