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
    1 decade ago
    Favorite Answer

    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.

  • 1 decade ago

    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

  • 1 decade ago

    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

  • 1 decade ago

    V = 4/3 π r³

    r = ³√( (1000*3) / (4π) )

    r = 6.2 cm

    A = 4 π r²

    A = 483.6 cm²

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  • 1 decade ago

    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

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