The <em>surface</em> area of the <em>larger</em> sphere is equal to 636.365 square centimeters.
<h3>How to determine the surface area of the sphere by the use of direct variation formulas</h3>
In this question we must estimate the <em>surface</em> area of the <em>smaller</em> sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the <em>surface</em> area is directly proportional to the square of radius, then the <em>volume</em> to <em>surface area</em> ratio is equal to:
V/A = k · r (1)
Where:
- r - Radius
- k - Proportionality constant
Then, we can derive the following relationship between the two spheres by eliminating the proportionality constant:
V/(A · r) = V'/(A' · R) (2)
Where:
- r - Radius of the smaller sphere.
- R - Radius of the larger sphere.
First, we need to determine the radii of the spheres:
Larger radius
R = ∛(3 · V' / 4π)
R = ∛(3 · 647 / 4π)
R ≈ 5.365 cm
Smaller sphere
r = ∛(3 · V / 4π)
r = ∛(3 · 87 / 4π)
r ≈ 2.749 cm
Lastly, we find the surface area of the larger sphere:
A · r · V' = A' · R · V
A' = (A · r · V') / (R · V)
A' = (167 · 2.749 · 647) / (5.365 · 87)
A' = 636.365 cm²
The <em>surface</em> area of the <em>larger</em> sphere is equal to 636.365 square centimeters.
To learn more on spheres: brainly.com/question/11374994
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Answer:
10m
Step-by-step explanation:
You could say six tenths.
Answer:
96
Step-by-step explanation: