Two spheres have surface areas of 100π units2 and 36π units2. if the volume of the larger sphere is π units3, determine the following measures. scale factor = __ radius of smaller sphere = __ units radius of larger sphere = __ units volume of smaller sphere = __π units3

The formula for the area of a sphere is ...

... A = 4πr²

Solving for r gives

... r = √(A/(4π)) = (1/2)√(A/π)

The formula for the volume of a sphere is ...

... V = (4/3)πr³

Comparing this to the area formula, we see that ...

... V = A·(r/3)

a) Scale factor = √(area ratio) = √(100π/(36π)) = 10/6 = 5/3

... The larger sphere is 5/3 the dimensions of the smaller sphere.

b) Radius of the smaller sphere is

... (1/2)√(36π/π) = 3 . . . units

c) Radius of the larger sphere is

... (1/2)√(100π/π) = 5 . . . units . . . . = (5/3)·3 units

d) Volume of the smaller sphere is

... V = A·r/3 = (36π)·(3/3) = 36π . . . units³

e) Volume of the larger sphere is

... V = A·r/3 = (100π)·(5/3) = 500π/3 . . . units³

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

x=half

step-by-step explanation: