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[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=\stackrel{\times 6}{6r} \end{cases}\implies V=\pi (6r)^2 h\implies V=\pi (6^2r^2) h \\\\\\ V=36~~\pi r^2 h\impliedby \textit{36 times the original volume}[/tex]
The effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36
Calculating the volume of a cylinder
From the question, we are to determine what effect multiplying radius by 6 would have on the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume of the cylinder
r is the radius
and h is the height
If the r is the radius and h is the height of the first cylinder,
Then, volume of the first cylinder will be
V = πr²h
For the new cylinder
radius = 6r
and h = h
Then, volume of the new cylinder will be
V₂ = π × (6r)² × h
V₂ = π × 36r² × h
V₂ = 36πr²h
The new volume is multiplied by a factor of 36
Hence, the effect that multiplying the radius by 6 would have on the volume of the cylinder is the volume would increase by a factor of 36.
Learn more on Calculating the volume of a cylinder here: https://brainly.com/question/18757852
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