Diameter of a sphere formula using volume
The diameter can be used to calculate the volume of a sphere. The diameter of a sphere is the length of the longest line inside the sphere that passes through its center. A sphere is a three-dimensional object that is spherical and fully symmetrical. A ball, a globe, and other spheres are examples. The volume of a sphere is the quantity of space contained within it (or) the sphere's holding capacity. We'll use the volume to calculate the diameter of a sphere in this post. You can get all Maths formulas on one-page visit the Maths Formulas section of HT.
The volume of a sphere with a diameter?
The volume V of the sphere of radius r can be computed using the formula V = (4/3) π r3. This is the formula for the radius-based volume of a sphere. We know that a sphere's diameter is twice its radius. d = 2r is the diameter. We get r = d/2 from this. V = (4/3) π (d/2)3 = (4/3) π (d3/8) = (πd3)/6 when this is substituted in the volume formula.V = (πd3)/6 is the volume of a sphere in terms of diameter (d).
Diameter of a sphere formula using volume
We learned the formula for calculating a sphere's volume (V) using its diameter in the previous section (d). Therefore, to get the diameter of a sphere using its volume, we may simply solve this formula for the diameter (d).
V = (πd3)/6
6V = πd3 (Multiplied both sides by 6)
6V/π = d3 (Divided both sides by π)
(6V/π)(1/3) = d (increased the power on both sides by 1/3.
Thus, d = (6V/π)(1/3) is the formula for a sphere's diameter using its volume.
Diameter of a sphere using volume calculation
Consider a sphere with a radius of r, a diameter of d, and a volume of V. The diameter of the sphere can be calculated in three ways using its volume:
Solve for r by substituting the value of V in the volume of a sphere formula in terms of radius, V = (4/3)πr3. Then use the formula d = 2r.
Solve for d by substituting the value of V in the volume of a sphere formula in terms of diameter, V = (πd3)/6.
Substitute volume for the value of V in the diameter of a sphere formula, d = (6V/π)(1/3)
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