What is the volume of a sphere with a diameter of 55.6m, rounded to the nearest tenth of a cubic meter? Answer: m^(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.Calculate Radius: Calculate the radius of the sphere. The diameter of the sphere is given as 55.6 meters. The radius is half of the diameter, so r = diameter / 2 = 55.6m / 2 = 27.8m.Substitute into Formula: Substitute the radius into the volume formula. V = (4/3)π(27.8m)^3Calculate Volume: Calculate the volume using the radius value. V = (4/3)π(27.8m)^3 = (4/3)π(27.8m * 27.8m * 27.8m) = (4/3)π(21483.92m^3)Evaluate Expression: Evaluate the expression to find the volume. V = (4/3)π(21483.92m^3) ≈ (4/3) * 3.14159 * 21483.92m^3 ≈ 35804.8m^3Round Volume: Round the volume to the nearest tenth of a cubic meter. The volume of the sphere is approximately 35804.8m^3, which is already rounded to the nearest tenth.

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What is the volume of a sphere with a diameter of
55.6m, rounded to the nearest tenth of a cubic meter?
Answer:
m^(3)

What is the volume of a sphere with a diameter of $55.6 \mathrm{~m}$ , rounded to the nearest tenth of a cubic meter? $\newline$ Answer: $\mathrm{m}^{3}$

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Math Problems

Grade 7

Convert between customary and metric systems

Full solution

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

55.6 \mathrm{~m}

, rounded to the nearest tenth of a cubic meter?

\newline

Answer:

\mathrm{m}^{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.
Calculate Radius: Calculate the radius of the sphere. $\newline$ The diameter of the sphere is given as $55.6$ meters. The radius is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{55.6m}{2} = 27.8m$ .
Substitute into Formula: Substitute the radius into the volume formula. $V = \left(\frac{4}{3}\right)\pi(27.8\,\text{m})^3$
Calculate Volume: Calculate the volume using the radius value. $V = \left(\frac{4}{3}\right)\pi(27.8\,\text{m})^3 = \left(\frac{4}{3}\right)\pi(27.8\,\text{m} \times 27.8\,\text{m} \times 27.8\,\text{m}) = \left(\frac{4}{3}\right)\pi(21483.92\,\text{m}^3)$
Evaluate Expression: Evaluate the expression to find the volume. $\newline$ $V = \frac{4}{3}\pi(21483.92m^3) \approx \frac{4}{3} \times 3.14159 \times 21483.92m^3 \approx 35804.8m^3$
Round Volume: Round the volume to the nearest tenth of a cubic meter. The volume of the sphere is approximately $35804.8\,\text{m}^3$ , which is already rounded to the nearest tenth.