The value of g in the 20 sided regular polygon is 54.
<h3>How to find the angles of a regular polygon?</h3>
If all the polygon sides and interior angles are equal, then they are known as regular polygons.
The polygon given is a 20 sided regular polygon and the measure of each angle is 3g degrees.
Therefore, let's find g.
The sum of interior angles of a 20 sided polygon is as follows:
180(n - 2) = 180(20 - 2) = 180(18) = 3240
Therefore,
each angle = 3240 / 20 = 162
Hence,
162 = 3g
g = 162 / 3
Therefore,
g = 54
learn more on regular polygon here: brainly.com/question/16992545
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False explanation..........
Answer:
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Answer:
![A_{f}=4\pi (\sqrt[3]{36} r)^{2}\\\\V_{f}=\frac{4}{3} \pi (36r^{3})](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29)
Step-by-step explanation:
In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:
![V_{1}=\frac{4}{3} \pi (r^{3})\\\\V_{2}=\frac{4}{3} \pi (2r)^{3}\\\\V_{3}=\frac{4}{3} \pi (3r)^{3}\\\\V_{f}=\frac{4}{3} \pi (r^{3}+(2r)^{3}+(3r)^{3})\\\\V_{f}=\frac{4}{3} \pi (r^{3}+8r^{3}+27r^{3})\\\\V_{f}=\frac{4}{3} \pi (36r^{3})\\\\V_{f}=\frac{4}{3} \pi R^{3}\\\\R=\sqrt[3]{36} r](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%29%5C%5C%5C%5CV_%7B2%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%282r%29%5E%7B3%7D%5C%5C%5C%5CV_%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%283r%29%5E%7B3%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B%282r%29%5E%7B3%7D%2B%283r%29%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B8r%5E%7B3%7D%2B27r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E%7B3%7D%5C%5C%5C%5CR%3D%5Csqrt%5B3%5D%7B36%7D%20r)
Now that we know the radii of the new sphere, we can calculate the surface area:
![A_{f}=4\pi R^{2}\\\\A_{f}=4\pi (\sqrt[3]{36} r)^{2}](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20R%5E%7B2%7D%5C%5C%5C%5CA_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D)
