What is the volume of a sphere with a diameter of 6.3 in, rounded to the nearest tenth of a cubic inch? Answer: in ^(3)

Calculate Radius: To find the volume of a sphere, we use the formula V = (4/3)πr^3, where r is the radius of the sphere. The radius is half of the diameter, so we first need to calculate the radius of the sphere with a diameter of 6.3 inches. Radius, r = Diameter / 2 = 6.3 in / 2 = 3.15 inPlug into Volume Formula: Now that we have the radius, we can plug it into the volume formula. V = (4/3)π(3.15 in)^3Calculate Volume: Next, we calculate the volume using the radius value. V = (4/3)π(3.15 in)^3 = (4/3)π(31.00375 in^3)Simplify Expression: We simplify the expression by calculating the numerical value. V ≈ (4/3) * 3.14159 * 31.00375 in^3 ≈ 129.847 in^3Round to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic inch. V ≈ 129.8 in^3 (rounded to the nearest tenth)

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What is the volume of a sphere with a diameter of 6.3 in, rounded to the nearest tenth of a cubic inch?
Answer: in
^(3)

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

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Grade 6

Evaluate variable expressions: word problems

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

6

3

\text{in}

, rounded to the nearest tenth of a cubic inch?

\newline

Answer:

\text{in}

^{3}

Calculate 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. The radius is half of the diameter, so we first need to calculate the radius of the sphere with a diameter of $6.3$ inches. $\newline$ Radius, $r = \frac{\text{Diameter}}{2} = \frac{6.3 \text{ in}}{2} = 3.15 \text{ in}$
Plug into Volume Formula: Now that we have the radius, we can plug it into the volume formula. $\newline$ $V = \frac{4}{3}\pi(3.15 \, \text{in})^3$
Calculate Volume: Next, we calculate the volume using the radius value. $V = \left(\frac{4}{3}\right)\pi(3.15 \text{ in})^3 = \left(\frac{4}{3}\right)\pi(31.00375 \text{ in}^3)$
Simplify Expression: We simplify the expression by calculating the numerical value. $\newline$ $V \approx \frac{4}{3} \times 3.14159 \times 31.00375 \, \text{in}^3 \approx 129.847 \, \text{in}^3$
Round to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic inch. $\newline$ $V \approx 129.8$ in $^3$ (rounded to the nearest tenth)