Exercise 49 Page 16

To find the side length of the jewelry box, let's first examine the net and the cube with a side length of a.

Net	Cube

Side Length and Area

We can find the surface area of one side of a cube with a side length of a by squaring its side length.

A= a^2

Total Surface Area

Since a cube has 6 sides, the surface area of a cube can be found by multiplying the area of one side A by 6. S=6A ⇒ S=6 a^2 Now, we can determine the dimensions of the jewelry box using the fact that its surface area is 300 square inches.

S=6a^2

Substitute

S= 300

300=6a^2

DivEqn

.LHS /6.=.RHS /6.

50=a^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(50)=a

RearrangeEqn

Rearrange equation

a=sqrt(50)

As a result, the side length of the jewelry box is sqrt(50) inches. Since the jewelry box has a cubic shape, its side length is the only dimension we need to find, as we get the volume by multiplying sqrt(50) by itself three times. Therefore, we can write the dimensions as a multiplication. sqrt(50)inches * sqrt(50)inches * sqrt(50)inches