What is the volume of a sphere with a diameter of 24.7m, 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 24.7 meters. The radius is half of the diameter, so r = diameter / 2 = 24.7m / 2 = 12.35m.Substitute radius: Substitute the radius into the volume formula. V = (4/3)π(12.35m)^3Calculate volume: Calculate the volume using the radius value. V = (4/3)π(12.35m)^3 = (4/3)π(12.35m * 12.35m * 12.35m)Perform multiplication: Perform the multiplication to find the volume before rounding. V ≈ (4/3)π(1881.6225m^3) ≈ (4/3) * 3.14159 * 1881.6225m^3 ≈ 4 * 3.14159 * 627.2075m^3 ≈ 7853.9817m^3Round volume: Round the volume to the nearest tenth of a cubic meter. V ≈ 7853.9817m^3 rounded to the nearest tenth is 7854.0m^3.

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What is the volume of a sphere with a diameter of
24.7m, rounded to the nearest tenth of a cubic meter?
Answer:
m^(3)

What is the volume of a sphere with a diameter of $24.7 \mathrm{~m}$ , 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

24.7 \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 $24.7$ meters. The radius is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{24.7\,\text{m}}{2} = 12.35\,\text{m}$ .
Substitute radius: Substitute the radius into the volume formula. $\newline$ $V = \frac{4}{3}\pi(12.35\,\text{m})^3$
Calculate volume: Calculate the volume using the radius value. $V = \left(\frac{4}{3}\right)\pi(12.35\,\text{m})^3 = \left(\frac{4}{3}\right)\pi(12.35\,\text{m} \times 12.35\,\text{m} \times 12.35\,\text{m})$
Perform multiplication: Perform the multiplication to find the volume before rounding. $\newline$ $V \approx \frac{4}{3}\pi(1881.6225m^3) \approx \frac{4}{3} \times 3.14159 \times 1881.6225m^3 \approx 4 \times 3.14159 \times 627.2075m^3 \approx 7853.9817m^3$
Round volume: Round the volume to the nearest tenth of a cubic meter. $V \approx 7853.9817\,\text{m}^3$ rounded to the nearest tenth is $7854.0\,\text{m}^3$ .