Question

The formula mc022-1.jpg 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 480 square meters than a cube with the surface area of 270 square meters?

Answer 1

This is the concept of scale factors; To get how much longer the length of one cube is compared to another, we are required to find their length;
The surface area of the cube is given by:
A=6a^2
Thus;
a=√(A/6)
The length of the cube with SA of 480 m^2 will be:
a=√(480/6)
a=8.944 m

The length of the cube with SA of 270 m^2
a=√(270/6)
a=6.71 m

The larger cube is longer than the smaller one by:
8.94-6.71=2.23 m

Answer 2

The difference between side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters is $\boxed{\sqrt5 }.$

Further explanation:

The formula for the surface area of the cube is given by,

$\boxed{{\text{Surface Area}} = 6{a^2}}$

Given:

The surface area of the cube with longer side is $480{\text{ }}{{\text{m}}^2}.$

The surface area of the cube with smaller side is $270{\text{ }}{{\text{m}}^2}.$

Explanation:

Let us consider that the side of larger cube be $x$ and the side of smaller cube be $y$.

The value of $x$ can be obtained as follows,

$\begin{aligned}6{x^2} &= 480\\{x^2} &=\frac{{480}}{6}\\{x^2}&= 80\\x&= \sqrt {80}\\x&= 4\sqrt5\\\end{aligned}$

The value of $y$ can be obtained as follows,

$\begin{aligned}6{y^2}&= 270\\{y^2}&= \frac{{270}}{6}\\{y^2}&= 45\\y&= \sqrt {45}\\y&= 3\sqrt5\\\end{aligned}$

The difference between the sides can be obtained as follows,

$\begin{aligned}x - y &= 4\sqrt 5 - 3\sqrt 5\\&= \sqrt5\\\end{aligned}$

The difference between side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters is $\boxed{\sqrt5 }.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of Derivatives

Keywords: Cube, longer side, surface area, formula, length of the side, 480 square meters, 270 square meters.