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The formula s= √SA/6 gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?

Respuesta :

Louli
Surface area of cube = 6 * (side)^2
side^2 = surface area / 6
side = sqrt (surface area / 6)

For the cube with area 1200 square inches:
side = sqrt(surface area / 6)
side = sqrt(1200 / 6) 
side = 14.1421 inches

For the cube with area 768 square inches:
side = sqrt(surface area / 6) 
side = sqrt(768 / 6) 
side = 11.3137 inches

difference between the two lengths = 14.1421 - 11.3137 = 2.8284 inches

Based on the above calculations, the side of the cube with surface area 1200 square inches is  2.8284  inches longer than the side of the cube with surface area 768 square inches

The difference in the side of a cube with a surface area of 1,200 square inches and a cube with a surface area of 768 square inches is 2.8284 in.

What is a cube?

A cube is a 3-dimensional shape whose all six faces are square.

Given to us

side, s= √SA/6

As the expression for the side of the cube is given, using the same, we will find the length of the two sides of the cube,

Length of the side of cube 1,

[tex]s = \sqrt{\dfrac{SA}{6}}[/tex]

[tex]s = \sqrt{\dfrac{1200}{6}}\\\\s = 14.1421\rm\ in[/tex]

Length of the side of cube 2,

[tex]s = \sqrt{\dfrac{SA}{6}}[/tex]

[tex]s = \sqrt{\dfrac{768}{6}}\\\\s = 11.3137\rm\ in[/tex]

The difference in the side of the cubeD = Length of the side of cube 1 - Length of the side of cube 2 = 14.1421 - 11.3137 = 2.8284 in.

Hence, the difference in the side of a cube with a surface area of 1,200 square inches and a cube with a surface area of 768 square inches is 2.8284 in.

Learn more about Cubes:

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