Sphere surface area?

Question

A sphere has a volume of 1000 cm^3. What is its surface area?

(How is the surface area of a sphere determined from its volume)

Answer 1

V = 4 π r³ / 3.
A = 4 π r².

From the volume, multiply by 0.75 (3/4) and divide by π. Find the cube root of this result and you'll have the radius.

To get the area, square the radius, and multiply by 4π.

V = 4 π r³ / 3.
3V / 4π = r³
[³√(3 V) / ³√(4 π)] = r
A = 4 π r²
A = 4 π [³√(3 V) / ³√(4 π)]²
A = 4 π ³√(3 V)² / ³√(4 π)²
A = 4 π ³√(3 V)² ³√(4 π) / 4π
A = ³√(9 V²) ³√(4π)
A = ³√(36 π V²), for any sphere.

For your sphere, V = 1000 cm³
A = ³√(36 π 1000000)
A = ³√(36000000 π)
A = 100 ³√(36 π), or approx. 483.597586 cm².

Answer 2

V = 4/3 * Pi r^3 (four thirds Pi r cubed)

1000 = 4/3 3.14 r^3

238.854 = r^3

6.205 = r, so the radius of the sphere is 6.205 cm.

The formula for the surface of a cube is SA = 4 Pi r^2
SA = 4 (3.14)(6.205)^2
SA = 483.585 cm^2

Answer 3

Equation for Volume of sphere is
V = 4/3(pi)(r^3)

Equation for Surface Area is
S = 4(pi)(r^2)

First find r using the top equation.
1000 cm^3 = 4/3(pi)(r^3)
(1000 cm^3)(3/4) = (pi)(r^3)
(1000 cm^3)(3/4)/(pi) = r^3
((1000 cm^3)(3/4)/(pi))^(1/3) = r
r = (5)(6/pi)^(1/3)) cm
r is about 6.2035 cm

Now plug that into the surface area formula
S = 4(pi)(6.2035 cm)^2)
S is exactly 100(36pi)^(1/3) cm^2
S is about 483.598 cm^2

Answer 4

V = 4/3 π r³
r = ³√( (1000*3) / (4π) )
r = 6.2 cm
A = 4 π r²
A = 483.6 cm²

Answer 5

V = (4 Pi/3)r^3 = (Pi/6)d^3
S = 4 Pi r^2 = Pi d^2

1000 = (pi/6)d^3
d^3 = 1000/(pi/6)
d^3 = (1000/1)/(pi/6)
d^3 = (1000/1)*(6/pi)
d^3 = (6000/pi)
d = cbrt(6000/pi)
d = about 12.41cm

S = Pi d^2
S = Pi * (cbrt(6000/pi))^2
S = 483.597586cm^2

ANS : about 483.6cm^2