What is the volume of a sphere with a diameter of 6.7 in, rounded to the nearest tenth of a cubic inch? Answer: in ^(3)

Identify formula for volume: Identify the formula for 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 6.7 inches. The radius is half of the diameter, so r = diameter / 2 = 6.7 inches / 2 = 3.35 inches.Substitute radius into formula: Substitute the radius into the volume formula. V = (4/3)π(3.35 inches)^3Calculate volume using radius: Calculate the volume using the radius value. V = (4/3)π(3.35 inches)^3 = (4/3)π(3.35 inches * 3.35 inches * 3.35 inches)Perform multiplication: Perform the multiplication. V = (4/3)π(37.595875 inches^3) ≈ (4/3) * 3.14159 * 37.595875 inches^3Calculate numerical value: Calculate the numerical value. V ≈ (4/3) * 3.14159 * 37.595875 inches^3 ≈ 4.18879 * 37.595875 inches^3 ≈ 157.464 cubic inchesRound volume: Round the volume to the nearest tenth of a cubic inch. V ≈ 157.5 cubic inches (rounded to the nearest tenth)

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What is the volume of a sphere with a diameter of 6.7 in, rounded to the nearest tenth of a cubic inch?
Answer: in
^(3)

What is the volume of a sphere with a diameter of $6$ . $7$ $\text{in}$ , rounded to the nearest tenth of a cubic inch? $\newline$ Answer: $\text{in}$ $^{3}$

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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

6

7

\text{in}

, rounded to the nearest tenth of a cubic inch?

\newline

Answer:

\text{in}

^{3}

Identify formula for volume: Identify the formula for 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 $6.7$ inches. The radius is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{6.7 \text{ inches}}{2} = 3.35$ inches.
Substitute radius into formula: Substitute the radius into the volume formula. $\newline$ $V = \frac{4}{3}\pi(3.35 \text{ inches})^3$
Calculate volume using radius: Calculate the volume using the radius value. $V = \frac{4}{3}\pi(3.35 \text{ inches})^3 = \frac{4}{3}\pi(3.35 \text{ inches} \times 3.35 \text{ inches} \times 3.35 \text{ inches})$
Perform multiplication: Perform the multiplication. $\newline$ $V = \left(\frac{4}{3}\right)\pi(37.595875 \text{ inches}^3) \approx \left(\frac{4}{3}\right) \times 3.14159 \times 37.595875 \text{ inches}^3$
Calculate numerical value: Calculate the numerical value. $\newline$ $V \approx \frac{4}{3} \times 3.14159 \times 37.595875$ inches $^3 \approx 4.18879 \times 37.595875$ inches $^3 \approx 157.464$ cubic inches
Round volume: Round the volume to the nearest tenth of a cubic inch. $V \approx 157.5$ cubic inches (rounded to the nearest tenth)