What is the volume of a sphere with a diameter of 8.2in, 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)πr³, 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 8.2 inches. Radius (r) = Diameter / 2 = 8.2 inches / 2 = 4.1 inches.Plug into Volume Formula: Now that we have the radius, we can plug it into the volume formula. V = (4/3)πr³ = (4/3)π(4.1 inches)³Calculate Volume: Next, we calculate the volume using the radius value. V = (4/3)π(4.1 inches)³ = (4/3)π(4.1³) = (4/3)π(68.921) cubic inchesPerform Multiplication: Now we perform the multiplication to find the volume. V = (4/3)π(68.921) = 91.8947π cubic inchesApproximate Volume: We can use the approximation π ≈ 3.14159 to calculate the volume numerically. V ≈ 91.8947 × 3.14159 ≈ 288.684 cubic inchesRound to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic inch as requested. V ≈ 288.7 cubic inches (rounded to the nearest tenth)

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What is the volume of a sphere with a diameter of
8.2in, rounded to the nearest tenth of a cubic inch?
Answer: in
^(3)

What is the volume of a sphere with a diameter of $8.2$ $\mathrm{in}$ , 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

Full solution

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

8.2

\mathrm{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 $8.2$ inches. $\newline$ Radius $r$ = Diameter / $2$ = $8.2$ inches / $2$ = $4.1$ inches.
Plug into Volume Formula: Now that we have the radius, we can plug it into the volume formula. $\newline$ $V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi(4.1 \text{ inches})^3$
Calculate Volume: Next, we calculate the volume using the radius value. $V = \left(\frac{$4$}{$3$}\right)\pi($4$.$1$ \text{ inches})^$3$ = \left(\frac{$4$}{$3$}\right)\pi($4$.$1$^$3$) = \left(\frac{$4$}{$3$}\right)\pi($68$.$921$) \text{ cubic inches}
Perform Multiplication: Now we perform the multiplication to find the volume. $V = \left(\frac{4}{3}\right)\pi(68.921) = 91.8947\pi$ cubic inches
Approximate Volume: We can use the approximation $\pi \approx 3.14159$ to calculate the volume numerically.$\newline$$V \approx 91.8947 \times 3.14159 \approx 288.684$ cubic inches
Round to Nearest Tenth: Finally, we round the volume to the nearest tenth of a cubic inch as requested. $\newline$$V \approx 288.7$ cubic inches (rounded to the nearest tenth)