What is the diameter of a hemisphere with a volume of 52079ft^(3), to the nearest tenth of a foot? Answer: ft

Identify Volume Formula: Identify the formula for the volume of a hemisphere. The volume (V) of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere.Solve for Radius: Solve the formula for the radius (r). We need to isolate r in the formula V = (2/3)πr³. To do this, we will divide both sides of the equation by (2/3)π. r³ = V / ((2/3)π)Plug in Volume: Plug in the given volume into the formula. We know the volume V = 52079 ft³. Now we substitute this value into the equation from Step 2. r³ = 52079 / ((2/3)π)Calculate Radius: Calculate the radius. r³ = 52079 / ((2/3)π) r³ = 52079 / (2π/3) r³ = 52079 * (3/(2π)) r³ ≈ 52079 * (3/(2*3.14159)) r³ ≈ 52079 * (3/6.28318) r³ ≈ 52079 * 0.47746 r³ ≈ 24865.5 Now we take the cube root of both sides to solve for r. r ≈ ³√24865.5 r ≈ 29.2 ftCalculate Diameter: Calculate the diameter of the hemisphere. The diameter (d) is twice the radius, so d = 2r. d = 2 * 29.2 ft d ≈ 58.4 ft

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What is the diameter of a hemisphere with a volume of
52079ft^(3), to the nearest tenth of a foot?
Answer:
ft

What is the diameter of a hemisphere with a volume of $52079 \mathrm{ft}^{3}$ , 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 hemisphere with a volume of

52079 \mathrm{ft}^{3}

, to the nearest tenth of a foot?

\newline

Answer:

\mathrm{ft}

Identify Volume Formula: Identify the formula for the volume of a hemisphere. $\newline$ The volume $V$ of a hemisphere is given by the formula $V = \frac{2}{3}\pi r^3$ , where $r$ is the radius of the hemisphere.
Solve for Radius: Solve the formula for the radius $r$ . We need to isolate $r$ in the formula $V = \frac{2}{3}\pi r^3$ . To do this, we will divide both sides of the equation by $\frac{2}{3}\pi$ . $r^3 = \frac{V}{\left(\frac{2}{3}\pi\right)}$
Plug in Volume: Plug in the given volume into the formula. $\newline$ We know the volume $V = 52079 \text{ ft}^3$ . Now we substitute this value into the equation from Step $2$ . $\newline$ $r^3 = \frac{52079}{\left(\frac{2}{3}\pi\right)}$
Calculate Radius: Calculate the radius. $\newline$ $r^3 = \frac{52079}{\left(\frac{2}{3}\right)\pi}$ $\newline$ $r^3 = \frac{52079}{\frac{2\pi}{3}}$ $\newline$ $r^3 = 52079 \times \left(\frac{3}{2\pi}\right)$ $\newline$ $r^3 \approx 52079 \times \left(\frac{3}{2 \times 3.14159}\right)$ $\newline$ $r^3 \approx 52079 \times \left(\frac{3}{6.28318}\right)$ $\newline$ $r^3 \approx 52079 \times 0.47746$ $\newline$ $r^3 \approx 24865.5$ $\newline$ Now we take the cube root of both sides to solve for r. $\newline$ $r \approx \sqrt[3]{24865.5}$ $\newline$ $r \approx 29.2$ ft
Calculate Diameter: Calculate the diameter of the hemisphere. $\newline$ The diameter $d$ is twice the radius, so $d = 2r$ . $\newline$ $d = 2 \times 29.2$ ft $\newline$ $d \approx 58.4$ ft