Math and Arithmetic
Geometry

# How do you find the volume and surface area of a cube?

The volume of a cube = a3

The surface area = 6a2

(a=one side of the square in a cube)

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## Related Questions

Write a c program to compute the surface area and volume of a cube

To tackle this you first need to know the equations for both volume and surface area. The surface area of a cube is 6x2 where x is the side length. The volume of the cube is x3. Thus x is the cube root of the volume. We can substitute this in to the surface area equation and say that the surface area of a cube is 6volume2/3 This can also be rearranged to say that the volume of the cube is (the surface area/6)1.5

Take the cube root of the volume to get the length of an edge. Square this number to get the area of a side, Multiply this by 6 to get the total surface area of the cube.

From the surface area, calculate the length of each side: area = 6 x side2.Once you know this side, you can get the cube of it, to obtain the volume.

Divide the surface area by six. That will give you the area of one face, which will be a perfect square. The square root of that number will give you the length of a side. The cube of the side will be the volume.

This should be solved in two steps. 1) Use the formula for the area of a cube, and solve for the length of a side of the cube. 2) Using this length, it is easy to find out the volume, with the formula for the volume of a cube.

Cube root the volume and square it multiplying it by 6 As for example if its volume was 27 then its cube root is 3 and 32*6 = 54 which is the cube's total surface area

If a is the side,lateral surface area of cube=4a2

The answer to your question is below along with a general formula so you can see where the answer comes from.The formula for the volume of a cube with side length L is L3The formula for the surface area comes from finding the area of one side of the cube and multiplying that by 6 since there are 6 sides. The area of one side is L2 sothe surface area is 6L2 .Now if we want ratio of surface area to volume for any cube, it would be 6L2 /L3This simplifies to 6/LSo in the case of a cube with side length 3 mm it is 6/3 or 2.Method 2 would be to find the surface area and volume for your cube only and then divide.The volume is 33 and the surface area is 6(32 ) so the ratio of surface area to volume is6(32 )/33 =2

The surface-area-to-volume ratio may be calculated as follows: -- Find the surface area of the shape. -- Find the volume of the shape. -- Divide the surface area by the volume. The quotient is the surface-area-to-volume ratio.

You would have to specify the shape for which we are finding these quantities. But let us say that it is a cube, which is the easiest. The length of an edge of the cube, multiplied by itself gives the area of a face, and multiplied by itself again gives the volume. So the cube root of the volume is the edge length, and then the square of the edge length is the surface area of one face of the cube, which multiplied by 6 gives the area of the entire cube.

The easiest way to find the volume of a cube is to find the length of its edgeand then cube that number.Here's how to find the length of the edge from the total surface area:-- A cube has 6 faces. If its total surface area is 96 square units, thenthe area of each face is 16 square units.-- Each face is a square. If the area of the square is 16 square units, thenthe side of the square is 4 units.But the side of the square face is the same as the edge of the cube !-- The volume of the cube is (4 x 4 x 4) = 64 cubic units.

If a side is Lcm long, L X L X L=Volume L=7cm Surface area of one face=49cm2 No of faces=6 Total area=49X6=294

512^1/3 = 8 (inch) = length per side of cube82 = 64 = (sq inches) Area per side. There are 6 sides in a cube.64*6=384 (sq inches) Answer384 square inches surface area in a cube of volume 512 cubic inches.

if you are finding the surface area of a cube, first find the area of one side by multiplying length X width and then multiply the area of one side of the cube by 6. that would be the surface area of the cube

The answer depends on what information you have about the cube. If, for example, you know the volume, V, then the surface area is 6*cuberoot(V)^2. If you have the lengths of an edge, s, then it is 6*s^2.

You find the surface area of a cube by using the formula 6e2. In this case, e=edge.

The formula for volume is side cubed, and the formula for a square's area is side squared, so you find the cube root of the volume and square your answer to find area.

The surface-area-to-volume ratio also called the surface-to-volume ratio and variously denoted sa/volor SA:V, is the amount of surface area per unit volume of an object or collection of objects. The surface-area-to-volume ratio is measured in units of inverse distance. A cube with sides of length a will have a surface area of 6a2 and a volume of a3. The surface to volume ratio for a cube is thus shown as .For a given shape, SA:V is inversely proportional to size. A cube 2 m on a side has a ratio of 3 m&minus;1, half that of a cube 1 m on a side. On the converse, preserving SA:V as size increases requires changing to a less compact shape.

If the length of an edge is x, the volume is x3 To find the rate of change of the volume with respect to x, differentiate: d(x3)/dx = 3x2 The area of one face is x2 There are six faces so the total surface area is 6x2 Therefore the rate of change of volume, 3x2 , is half of 6x2 , the surface area.

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