Question
the surface area of a solid sphere is 616. calculate its radius
Answers
Answered by
GPT-4o mini
The formula for the surface area \( A \) of a sphere is given by:
\[
A = 4\pi r^2
\]
where \( r \) is the radius of the sphere. To find the radius when the surface area is 616, we can set up the equation:
\[
4\pi r^2 = 616
\]
Now, we can solve for \( r^2 \):
1. Divide both sides by \( 4\pi \):
\[
r^2 = \frac{616}{4\pi}
\]
2. Simplifying \( \frac{616}{4} \):
\[
\frac{616}{4} = 154
\]
So, we have:
\[
r^2 = \frac{154}{\pi}
\]
3. Now take the square root of both sides to find \( r \):
\[
r = \sqrt{\frac{154}{\pi}}
\]
Now, substituting the value of \( \pi \) (approximately 3.14):
\[
r \approx \sqrt{\frac{154}{3.14}} \approx \sqrt{49} \approx 7
\]
Thus, the radius \( r \) of the sphere is approximately \( 7 \) units.
\[
A = 4\pi r^2
\]
where \( r \) is the radius of the sphere. To find the radius when the surface area is 616, we can set up the equation:
\[
4\pi r^2 = 616
\]
Now, we can solve for \( r^2 \):
1. Divide both sides by \( 4\pi \):
\[
r^2 = \frac{616}{4\pi}
\]
2. Simplifying \( \frac{616}{4} \):
\[
\frac{616}{4} = 154
\]
So, we have:
\[
r^2 = \frac{154}{\pi}
\]
3. Now take the square root of both sides to find \( r \):
\[
r = \sqrt{\frac{154}{\pi}}
\]
Now, substituting the value of \( \pi \) (approximately 3.14):
\[
r \approx \sqrt{\frac{154}{3.14}} \approx \sqrt{49} \approx 7
\]
Thus, the radius \( r \) of the sphere is approximately \( 7 \) units.