Answers

1. The surface area of the larger sphere is equal to 636.365 square centimeters.

   How to determine the surface area of the sphere by the use of direct variation formulas

   In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area 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 surface area of the larger sphere is equal to 636.365 square centimeters.

   To learn more on spheres: https://brainly.com/question/11374994

   #SPJ1

   Reply