What is the volume of a sphere with a diameter of 48.6ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(3)

Find Radius: To find the volume of a sphere, we use the formula V = (4/3)πr³, where r is the radius of the sphere. Since the diameter is given, we first need to find the radius by dividing the diameter by 2. Radius (r) = Diameter / 2 = 48.6 ft / 2Calculate Radius: Now, let's calculate the radius. r = 48.6 ft / 2 = 24.3 ftSubstitute and Calculate Volume: Next, we will substitute the radius into the volume formula and calculate the volume. V = (4/3)π(24.3 ft)³Calculate Volume with Radius: Let's calculate the volume using the radius we found. V = (4/3)π(24.3 ft)³ = (4/3)π(24.3 ft × 24.3 ft × 24.3 ft)Perform Radius Cubed Multiplication: Now, we perform the multiplication for the radius cubed. (24.3 ft)³ = 24.3 ft × 24.3 ft × 24.3 ft = 14367.87 ft³Multiply by (4/3)π: We then multiply this result by (4/3)π to get the volume. V = (4/3)π × 14367.87 ft³Calculate Numerical Value: Now, we calculate the numerical value for the volume. V ≈ (4/3) × 3.14159 × 14367.87 ft³ ≈ 4.18879 × 14367.87 ft³ ≈ 60194.217 ft³Round to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic foot as asked in the question prompt. V ≈ 60194.2 ft³

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What is the volume of a sphere with a diameter of
48.6ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a sphere with a diameter of $48.6 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Full solution

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

48.6 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{3}

Find Radius: To find the volume of a sphere, we use the formula $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere. Since the diameter is given, we first need to find the radius by dividing the diameter by $2$ . $\newline$ Radius $r$ = Diameter / $2$ = $\frac{48.6 \text{ ft}}{2}$
Calculate Radius: Now, let's calculate the radius. $r = \frac{48.6 \, \text{ft}}{2} = 24.3 \, \text{ft}$
Substitute and Calculate Volume: Next, we will substitute the radius into the volume formula and calculate the volume. $\newline$ $V = \frac{4}{3}\pi(24.3 \, \text{ft})^3$
Calculate Volume with Radius: Let's calculate the volume using the radius we found. $\newline$ $V = \frac{4}{3}\pi(24.3 \, \text{ft})^3 = \frac{4}{3}\pi(24.3 \, \text{ft} \times 24.3 \, \text{ft} \times 24.3 \, \text{ft})$
Perform Radius Cubed Multiplication: Now, we perform the multiplication for the radius cubed. $\newline$ $(24.3 \, \text{ft})^3 = 24.3 \, \text{ft} \times 24.3 \, \text{ft} \times 24.3 \, \text{ft} = 14367.87 \, \text{ft}^3$
Multiply by $(\frac{4}{3})\pi$ : We then multiply this result by $(\frac{4}{3})\pi$ to get the volume. $\newline$ $V = (\frac{4}{3})\pi \times 14367.87 \, \text{ft}^3$
Calculate Numerical Value: Now, we calculate the numerical value for the volume. $V \approx \left(\frac{4}{3}\right) \times 3.14159 \times 14367.87 \text{ ft}^3 \approx 4.18879 \times 14367.87 \text{ ft}^3 \approx 60194.217 \text{ ft}^3$
Round to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic foot as asked in the question prompt. $V \approx 60194.2$ ft $^3$