IDNLearn.com provides a user-friendly platform for finding answers to your questions. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.
Sagot :
To find the diameter of a sphere when the surface area is given as [tex]\(50.27 \, m^2\)[/tex], follow these steps:
1. Understand the formula for the surface area of a sphere:
[tex]\[ A = 4 \pi r^2 \][/tex]
where [tex]\(A\)[/tex] is the surface area and [tex]\(r\)[/tex] is the radius of the sphere.
2. Rearrange the formula to solve for the radius ([tex]\(r\)[/tex]):
[tex]\[ r^2 = \frac{A}{4 \pi} \][/tex]
[tex]\[ r = \sqrt{\frac{A}{4 \pi}} \][/tex]
3. Substitute the given surface area [tex]\(A = 50.27 \, m^2\)[/tex] into the formula:
[tex]\[ r = \sqrt{\frac{50.27}{4 \pi}} \][/tex]
4. Calculate the value inside the square root and then take the square root to find [tex]\(r\)[/tex]:
- The calculation step isn't shown here, but we know the numerical result for [tex]\(r\)[/tex] is approximately [tex]\(2.0000907163368256 \, m\)[/tex].
5. Determine the diameter of the sphere:
- The diameter ([tex]\(d\)[/tex]) of a sphere is twice the radius ([tex]\(r\)[/tex]):
[tex]\[ d = 2r \][/tex]
6. Substitute the radius back into the diameter formula:
[tex]\[ d = 2 \times 2.0000907163368256 \, m \][/tex]
[tex]\[ d = 4.000181432673651 \, m \][/tex]
Since the calculated diameter is very close to [tex]\(4 \, m\)[/tex], the closest answer from the provided options is:
[tex]\[ \boxed{4 \, m} \][/tex]
So, the diameter of the sphere, given the surface area of [tex]\(50.27 \, m^2\)[/tex], is approximately [tex]\(4 \, m\)[/tex].
1. Understand the formula for the surface area of a sphere:
[tex]\[ A = 4 \pi r^2 \][/tex]
where [tex]\(A\)[/tex] is the surface area and [tex]\(r\)[/tex] is the radius of the sphere.
2. Rearrange the formula to solve for the radius ([tex]\(r\)[/tex]):
[tex]\[ r^2 = \frac{A}{4 \pi} \][/tex]
[tex]\[ r = \sqrt{\frac{A}{4 \pi}} \][/tex]
3. Substitute the given surface area [tex]\(A = 50.27 \, m^2\)[/tex] into the formula:
[tex]\[ r = \sqrt{\frac{50.27}{4 \pi}} \][/tex]
4. Calculate the value inside the square root and then take the square root to find [tex]\(r\)[/tex]:
- The calculation step isn't shown here, but we know the numerical result for [tex]\(r\)[/tex] is approximately [tex]\(2.0000907163368256 \, m\)[/tex].
5. Determine the diameter of the sphere:
- The diameter ([tex]\(d\)[/tex]) of a sphere is twice the radius ([tex]\(r\)[/tex]):
[tex]\[ d = 2r \][/tex]
6. Substitute the radius back into the diameter formula:
[tex]\[ d = 2 \times 2.0000907163368256 \, m \][/tex]
[tex]\[ d = 4.000181432673651 \, m \][/tex]
Since the calculated diameter is very close to [tex]\(4 \, m\)[/tex], the closest answer from the provided options is:
[tex]\[ \boxed{4 \, m} \][/tex]
So, the diameter of the sphere, given the surface area of [tex]\(50.27 \, m^2\)[/tex], is approximately [tex]\(4 \, m\)[/tex].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.