The volume inside is 27 cu. ft.
The surface area of a cube is the area of each face of the cube added together. There are 6 faces on a cube; 54/6 = 9 sq. ft. for each face of the cube.
Each face of a cube is a square, whose area is given by A=s²:
9 = s²
Take the square root of both sides:
√9 = √s²
3 = s
Each side of the square, or edge of the cube, is 3 ft.
This makes the volume 3(3)(3) = 27 cu. ft.
Answer:

Step-by-step explanation:
Another way to look at this question is: We make 5/6 yards of fabric from each pair of shorts. How many shorts do we need to make 35 yards of fabric.
So, we need to solve this equation for
:
.
We can multiply both sides of the equation by
to get
.
We then divide by
on both sides to get
.
So, we can make
pairs of soccer shorts.
Answer:

Step-by-step explanation:
<u>Given</u>:

The <u>sigma notation</u> means to find the sum of the given <u>geometric series</u> where the first term is when n = 1 and the last term is when n = ∞.
To find the <u>first term</u> in the series, substitute n = 1 into the expression:

The <u>common ratio</u> of the geometric series can be found by dividing one term by the previous term:

As | r | < 1 the series is <u>convergent.</u>
When a series is convergent, we can find its sum to infinity (the limit of the series).
<u>Sum to infinity formula</u>:

where:
- a is the first term in the series
- r is the common ratio
Substitute the found values of a and r into the formula:

Therefore:

Learn more about Geometric Series here:
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