Asked by DL
Marcus is making spherical soaps for sale in his online store the surface area of a soap is 63.585 in
Answers
Answered by
GPT-4o mini
To find the radius of the spherical soap given the surface area, we can use the formula for the surface area of a sphere:
\[
A = 4\pi r^2
\]
where \( A \) is the surface area and \( r \) is the radius. In this case, we know that the surface area \( A \) is \( 63.585 \) square inches.
We can rearrange the formula to solve for the radius \( r \):
\[
r^2 = \frac{A}{4\pi}
\]
Now, substituting the given surface area into the formula, we have:
\[
r^2 = \frac{63.585}{4\pi}
\]
Calculating \( 4\pi \):
\[
4\pi \approx 4 \times 3.14159 \approx 12.56636
\]
Now we can continue with the calculation:
\[
r^2 \approx \frac{63.585}{12.56636} \approx 5.06
\]
To find \( r \), we take the square root of \( r^2 \):
\[
r \approx \sqrt{5.06} \approx 2.25 \text{ inches}
\]
So, the radius of the spherical soap is approximately \( 2.25 \) inches.
\[
A = 4\pi r^2
\]
where \( A \) is the surface area and \( r \) is the radius. In this case, we know that the surface area \( A \) is \( 63.585 \) square inches.
We can rearrange the formula to solve for the radius \( r \):
\[
r^2 = \frac{A}{4\pi}
\]
Now, substituting the given surface area into the formula, we have:
\[
r^2 = \frac{63.585}{4\pi}
\]
Calculating \( 4\pi \):
\[
4\pi \approx 4 \times 3.14159 \approx 12.56636
\]
Now we can continue with the calculation:
\[
r^2 \approx \frac{63.585}{12.56636} \approx 5.06
\]
To find \( r \), we take the square root of \( r^2 \):
\[
r \approx \sqrt{5.06} \approx 2.25 \text{ inches}
\]
So, the radius of the spherical soap is approximately \( 2.25 \) inches.