geometry question?

Question

(pie) this is the sign for pie.

The volumes of two spheres are 327(pie) mm3
and 8829(pie) mm3.What is the ratio of their
surface areas?

need help...and not sure of my answer

Answer 1

It's pi, not pie.

Since the radius of a sphere = [(3V)/(4pi)]^(1/3), the two radii are:

r1 = [3(327)/(4*pi)]^(1/3) = 4.273854319 mm
r2 = [3(8829)/(4*pi)]^(1/3) = 12.82156296 mm

The two surface areas are:

SA1 = 4*pi*(r1)^2 = 229.5351987 mm^2
SA2 = 4*pi*(r2)^2 = 2065.816788 mm^2

Their ratio is: 229.5351987 / 2065.816788 = 1/9

Answer 2

You need to take the cube root of each of your volumes. That gives you the scale factor. Then square that answer, and you have the area ratio.

Answer 3

v = volume smaller sphere
V = volume larger sphere
r = radius smaller sphere
R = radius larger sphere
s = surface area smaller sphere
S = surface area larger sphere

v = 327π mm³
V = 8829π mm³

v = 4πr³/3
V = 4πR³/3

v/V = (4πr³/3) / (4πR³/3) = r³ / R³ = 327π / (8829π) = 1/27
r³ / R³ = 1/27
r/R = 1/3

s = 4πr²
S = 4πR²

s/S = 4πr² / (4πR²) = r² / R²

r/R = 1/3
r² / R² = (1/3)² = 1/9

s/S = r² / R² = 1/9

The ratio of their surface areas is 1/9.

Answer 4

(327/8829)^(2/3)

Answer 5

Yeah,what they said.