The volume of the cylinder is the amount of vinyl liner it can contain.
The diameter of the swimming pool is 4 feet.
Given that:
[tex]h = 4[/tex] --- height
The volume (V) of a cylinder is:
[tex]V = \pi r^2 h[/tex]
The amount of vinyl liner used for the large pool is not given. So, I will make an assumption.
Assume the amount used for the large pool is 35 cubic feet.
From the question, we understand that 1.5 of this amount is used for the new pool.
So:
[tex]V = 1.5 \times 35ft^3[/tex]
[tex]V = 52.5ft^3[/tex]
The volume equation becomes
[tex]V = \pi r^2 h[/tex]
[tex]52.5 = \pi r^2 h[/tex]
Substitute 4 for h and 3.143 for [tex]\pi[/tex]
[tex]52.5 = 3.143 \times r^2 \times 4[/tex]
Solve for [tex]r^2[/tex]
[tex]r^2 = \frac{52.5}{3.143 \times 4}[/tex]
[tex]r^2 = \frac{52.5}{12.572}[/tex]
[tex]r^2 = 4.1759[/tex]
Take positive square roots
[tex]r = 2.0435[/tex]
Multiply both sides by 2 to calculate diameter (d)
[tex]2r = 2 \times 2.0435[/tex]
[tex]2r = 4.087[/tex]
Rewrite as:
[tex]d = 4.087[/tex]
[tex]d = 4[/tex] -- approximated
Hence, the diameter of the pool (using the assumed volume) is approximately 4 feet
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