How To Find Service Area With Volume

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The volume of a three-dimensional shape is a measurement of the space within the shape and is determined by multiplying the length, width, and height. A cube is a three-dimensional shape in which the length, width, and pinnacle are equal. Thus, information technology is easy to observe the volume of a cube given the length of one edge. You tin also detect the book using the surface area, from which you tin derive the length of one edge.

i
Fix the formula for the surface area of a cube. The formula is $surfacearea=6x^{2}$ , where $x$ equals the length of one border of the cube.^[1]
- To observe the volume of a cube, yous need to multiply its three dimensions (length, width, top) together.^[2] These dimensions correspond to the length of the edges of the cube. Since all the dimensions (edges) of a cube are the same, in club to observe the volume of the cube, you lot first accept to make up one's mind the length of 1 of its edges. Since finding the surface expanse of a cube also requires the length of one edge, if you know the surface area, yous can work backwards to find the length of 1 border, then use the border length to piece of work forwards to find the volume.
2

Plug the surface expanse of the cube into the formula. This information should be given.

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3

Divide the surface area past 6. This will requite you the value of $10^{ii}$ .
4

Find the square root. This will requite you the value of $ten$ , or the length of ane edge of the cube.

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ane

Gear up up the formula for the volume of a cube. The formula is $five=ten^{3}$ , where $five$ equals the book of the cube, and $x$ equals the length of one border.^[three]
two
Plug the length of one border into the formula. You should have already calculated this from the given surface expanse.
- For example, if one edge of a cube is 4 centimeters, then your formula volition look like this:
  $5=4^{iii}$ .
3

Cube the length of 1 edge. To do this, you lot tin utilize a figurer, or just multiply x past itself three times. This will give yous the volume of your cube, in cubic units.

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Question

What nearly a rectangular prism? Would it yet be the same?

Non quite. The formula is slightly different. Assuming you know the length, width and superlative of the prism (l, w, and h), y'all would multiply the three values together to get the book, or you would find twice the sum of (lw + lh + wh) to find the area. If you know simply 2 of those values, simply you besides know either the book or the expanse, y'all can work backwards to find the unknown value.
Question

The volume of a cube is 64 mm^iii. How practice I calculate the area of ane of its faces?

The length of an edge is the cube root of 64, which is four mm. The face area is 4² = 16 sq mm.
Question

What is the volume of a cube with a surface expanse of 78 inches?

Kickoff y'all need to find the length of one edge using the formula for surface area: 78 = 6x^ii 13 = x^2 iii.61 inches = x At present that you know the length of one border, you lot can plug this value into the formula for volume of a cube: v = 3.61^iii v = 3.61 x iii.61 x 3.61 5 = 47.05 cubic inches

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Commodity Summary X

To find the volume of a cube from its expanse, first utilize the formula for surface area to discover the length of 1 side of your cube. To do this, plug the surface area you lot're given into the formula, which is surface area = 6x^2, where x is the length of i side of the cube. So, solve for x. Y'all tin then find the volume of your cube by using the formula five = ten^iii where v is volume and ten is the number you got previously for the length of one side of your cube. To meet an example of how to find the book of a cube from its expanse, scroll downwardly!

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