What is the volume of a sphere with a diameter of 34.5ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(3)

Identify Formula: Identify the formula to calculate the volume of a sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.Convert Diameter to Radius: Convert the diameter to radius. Since the diameter is 34.5 feet, the radius r is half of the diameter. Therefore, r = 34.5 / 2.Calculate Radius: Calculate the radius. r = 34.5 feet / 2 = 17.25 feet.Substitute Radius into Formula: Substitute the radius into the volume formula. V = (4/3)π(17.25)^3Calculate Volume Using Radius: Calculate the volume using the radius. V = (4/3)π(17.25)^3 ≈ (4/3)π(5136.875)Evaluate Expression: Evaluate the expression to find the volume. V ≈ (4/3)π(5136.875) ≈ 4π(1712.29166667) ≈ 4π(1712.3) when rounded to the nearest tenth.Calculate Approximate Volume: Calculate the approximate volume. V ≈ 4π(1712.3) ≈ 4 * 3.1416 * 1712.3 ≈ 21544.1 cubic feet when rounded to the nearest tenth.

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What is the volume of a sphere with a diameter of
34.5ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a sphere with a diameter of $34.5 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Grade 7

Convert between customary and metric systems

Full solution

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

34.5 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{3}

Identify Formula: Identify the formula to calculate the volume of a sphere. $\newline$ The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius of the sphere.
Convert Diameter to Radius: Convert the diameter to radius. $\newline$ Since the diameter is $34.5$ feet, the radius $r$ is half of the diameter. Therefore, $r = \frac{34.5}{2}$ .
Calculate Radius: Calculate the radius. $r = \frac{34.5 \text{ feet}}{2} = 17.25 \text{ feet}$ .
Substitute Radius into Formula: Substitute the radius into the volume formula. $V = \frac{4}{3}\pi(17.25)^3$
Calculate Volume Using Radius: Calculate the volume using the radius. $V = \frac{4}{3}\pi(17.25)^3 \approx \frac{4}{3}\pi(5136.875)$
Evaluate Expression: Evaluate the expression to find the volume. $\newline$ $V \approx \frac{4}{3}\pi(5136.875) \approx 4\pi(1712.29166667) \approx 4\pi(1712.3)$ when rounded to the nearest tenth.
Calculate Approximate Volume: Calculate the approximate volume. $V \approx 4\pi(1712.3) \approx 4 \times 3.1416 \times 1712.3 \approx 21544.1$ cubic feet when rounded to the nearest tenth.