Question

Find the missing dimension of the cylinder. Volume = 3785 cm^3 height is 19 cm i need to find the radius
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Answer 1

Answer:

r ≈ 7.963 cm

Step-by-step explanation:

Given the following dimensions of a cylinder:

Volume (V) = 3785 cm³

Height (h) = 19 cm

In order to find the value of the radius, it is necessary to determine the formula for finding the radius of a cylinder.

The formula for finding the volume of a cylinder is:  V = πr ²h

To isolate the radius, start by dividing both sides by π × h :

$\mathsf{\frac{V} {\pi\times\:h}\:=\:\frac{\pi\:r^{2}\:h} {\pi\times\:h}}$

$\mathsf{\frac{V} {\pi\times\:h}\:=\:r^{2}}$

Next, take the square root of both sides to isolate r :

$\mathsf{\sqrt{\frac{V}{\pi\times\:h}} = \sqrt{r^{2}}}$

$\mathsf{\:r\:=\:\sqrt{\frac{V}{\pi\times\:h}}}$

Now, we can finally substitute the given values into the formula for radius, r:

$\mathsf{\:r\:=\:\sqrt{\frac{3785}{\pi\times\:19}}}$

r ≈ 7.963 cm

Therefore, the radius of the cylinder is 7.963 cm.