Q: When a cube is tripled in size the surface area is?

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The cube's surface area consists of six squares; you can simply add the area of each of the squares. Note that each of the squares has the same size.

When you change the linear size it changes the areas by the square and the volume of the cube.

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−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.

This Wikipedia passage should be able to help you out. Note that this is just a cube and other shapes such as spheres will have a different ratio.(From Wikipedia "Surface Area to Volume Ratio")The surface-area-to-volume ratio has physical dimension L−1 (inverse length) and is therefore expressed in units of inverse distance. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm2 and a volume of 1 cm3. The surface to volume ratio for this cube is thus{\displaystyle {\mbox{SA:V}}={\frac {6~{\mbox{cm}}^{2}}{1~{\mbox{cm}}^{3=6~{\mbox{cm}}^{-1}}. For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm−1, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases requires changing to a less compact shape.

If they are all the same size, the surface area is just the total surface area, which is 6 (faces) x edge x edge - that is the area of one face, (the length of one edge times itself as cubes have square faces) x the number of faces (6) x the number of cubes (3). Then subtract fom this the area not exposed, which is the top face of the bottom cube, top and bottom of the middle cube and bottom face of the top cube - so that's 4 faces. So the formula boils down to: 6 x 3 x edge x edge - 4 x edge x edge ... or ... 14 edge² If they are different sizes: 1. Work out the total area of each cube. 2. Between the bottom and middle cube, take the smaller and that face is hidden on both cubes, so subtract twice this face. 3. Do the same for the top and middle cubes.

Related questions

Surface area also decreases

The cube 3 cm on a side has the greater surface area.

The ratio of the surface area of a cube to its volume is inversely proportional to the length of its side.

The Bigger Cube?

The cube's surface area consists of six squares; you can simply add the area of each of the squares. Note that each of the squares has the same size.

There is no specific cube size mentioned here, however; the formula to find size of the cube is 6a2 (square). Thus if the side is 8", the surface area would be 6 x 8 x 6 = 384.

The surface area of a sphere is directly proportional to the square of its radius. A ∝ r2 r = 3k A ∝ (3k)2 A ∝ 9k2 therefore, the surface area will become 9 times the size

starting size n, surface area = 6 x n2; starting size 2n surface area 6 x 4n2 so surface area would be quadrupled.

To find the surface area of a cube you find the area of one side then you multiply that by six because each side is exactly the same size.

It doesn't matter what the unit of measurement is, or what size the cube is. If the length of the side of the cube is 'S' units, then the volume is S3 and the surface area is 6S2. The ratio of volume to surface area is (S3/6S2) = S/6 units. For this one, the ratio is 1/6 cm.

Suppose the cube has edges of length x. Then the area of each face (side) is x2. There are six faces so the total surface area is 6x2. The volume of the cube is x3. So 6x2 = x3 DIviding both sides by x2 gives x = 6.

When you change the linear size it changes the areas by the square and the volume of the cube.