# Sphere surface area?

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)

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• Anonymous

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.

• 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

• 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

Now plug that into the surface area formula

S = 4(pi)(6.2035 cm)^2)

S is exactly 100(36pi)^(1/3) cm^2

• V = 4/3 π r³

r = ³√( (1000*3) / (4π) )

r = 6.2 cm

A = 4 π r²

A = 483.6 cm²

• 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)