What is the volume of a sphere with a diameter of 2.3ft, 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. First, we need to find the radius of the sphere. The radius is half of the diameter. Radius (r) = Diameter / 2 r = 2.3 ft / 2Calculate Radius: Now, let's calculate the radius. r = 2.3 ft / 2 r = 1.15 ftSubstitute and Calculate Volume: Next, we will substitute the radius into the volume formula and calculate the volume. V = (4/3)π(1.15 ft)³Calculate Volume: Now, we calculate the volume using the value of the radius. V = (4/3)π(1.15 ft)³ V ≈ (4/3) * 3.14159 * (1.15 ft)³ V ≈ 4.18879 * 1.521375 ft³Perform Multiplication: Let's perform the multiplication to find the volume. V ≈ 4.18879 * 1.521375 ft³ V ≈ 6.3717 ft³Round Volume: Finally, we round the volume to the nearest tenth of a cubic foot. V ≈ 6.4 ft³

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What is the volume of a sphere with a diameter of
2.3ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a sphere with a diameter of $2.3 \mathrm{ft}$ , 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

2.3 \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. First, we need to find the radius of the sphere. The radius is half of the diameter. $\newline$ Radius ( $r$ ) = Diameter / $2$ $\newline$ $r = \frac{2.3 \text{ ft}}{2}$
Calculate Radius: Now, let's calculate the radius. $\newline$ $r = \frac{2.3 \, \text{ft}}{2}$ $\newline$ $r = 1.15 \, \text{ft}$
Substitute and Calculate Volume: Next, we will substitute the radius into the volume formula and calculate the volume. $V = \frac{4}{3}\pi(1.15 \, \text{ft})^3$
Calculate Volume: Now, we calculate the volume using the value of the radius. $\newline$ $V = \frac{4}{3}\pi(1.15 \, \text{ft})^3$ $\newline$ $V \approx \frac{4}{3} \times 3.14159 \times (1.15 \, \text{ft})^3$ $\newline$ $V \approx 4.18879 \times 1.521375 \, \text{ft}^3$
Perform Multiplication: Let's perform the multiplication to find the volume. $\newline$ $V \approx 4.18879 \times 1.521375 \, \text{ft}^3$ $\newline$ $V \approx 6.3717 \, \text{ft}^3$
Round Volume: Finally, we round the volume to the nearest tenth of a cubic foot. $V \approx 6.4 \, \text{ft}^3$