What is the diameter of a sphere with a volume of 54147ft^(3), to the nearest tenth of a foot? Answer: ft

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. The formula for the volume (V) of a sphere in terms of its radius (r) is V = (4/3)πr³.Set Up Equation: Set up the equation to solve for the radius. We have the volume of the sphere, so we can set up the equation 54147 = (4/3)πr³.Solve for Radius: Solve for the radius (r). To isolate r³, we need to multiply both sides of the equation by the reciprocal of (4/3)π. r³ = 54147 / ((4/3)π)Calculate r³: Calculate the value of r³. r³ = 54147 / ((4/3)π) ≈ 54147 / (4.18879) ≈ 12924.3Cube Root for r: Take the cube root of both sides to solve for r. r ≈ ³√12924.3 ≈ 23.4 feetRecall Diameter Formula: Recall that the diameter (d) is twice the radius. d = 2rCalculate Diameter: Calculate the diameter. d = 2 * 23.4 ≈ 46.8 feet

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What is the diameter of a sphere with a volume of
54147ft^(3), to the nearest tenth of a foot?
Answer:
ft

What is the diameter of a sphere with a volume of $54147 \mathrm{ft}^{3}$ , to the nearest tenth of a foot? $\newline$ Answer: $\mathrm{ft}$

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Grade 7

Convert between customary and metric systems

Full solution

Q. What is the diameter of a sphere with a volume of

54147 \mathrm{ft}^{3}

, to the nearest tenth of a foot?

\newline

Answer:

\mathrm{ft}

Recall Sphere Volume Formula: Recall the formula for the volume of a sphere. $\newline$ The formula for the volume $V$ of a sphere in terms of its radius $r$ is $V = \frac{4}{3}\pi r^3$ .
Set Up Equation: Set up the equation to solve for the radius. $\newline$ We have the volume of the sphere, so we can set up the equation $54147 = \left(\frac{4}{3}\right)\pi r^3$ .
Solve for Radius: Solve for the radius $r$ . To isolate $r^3$ , we need to multiply both sides of the equation by the reciprocal of $(4/3)\pi$ . $r^3 = \frac{54147}{\left(\frac{4}{3}\pi\right)}$
Calculate $r^3$ : Calculate the value of $r^3$ . $r^3 = \frac{54147}{(\frac{4}{3})\pi} \approx \frac{54147}{4.18879} \approx 12924.3$
Cube Root for r: Take the cube root of both sides to solve for r. $\newline$ $r \approx \sqrt[3]{12924.3} \approx 23.4$ feet
Recall Diameter Formula: Recall that the diameter $d$ is twice the radius. $d = 2r$
Calculate Diameter: Calculate the diameter. $d = 2 \times 23.4 \approx 46.8$ feet