What is the volume of a hemisphere with a diameter of 5m, rounded to the nearest tenth of a cubic meter? Answer: m^(3)

Find Radius: First, we need to find the radius of the hemisphere. The radius is half of the diameter. Given diameter = 5m, so radius r = diameter / 2 = 5m / 2 = 2.5m.Calculate Volume of Sphere: Next, we use the formula for the volume of a sphere, which is V = (4/3)πr^3, and then we will take half of that volume to find the volume of the hemisphere since a hemisphere is half of a sphere.Calculate Volume of Sphere: Now, we calculate the volume of the sphere using the radius we found. V_sphere = (4/3)π(2.5m)^3Take Half of Volume: Perform the calculation for the volume of the sphere. V_sphere = (4/3)π(2.5m)^3 = (4/3)π(15.625m^3) = 20.833333...π m^3Approximate Pi: Since we need the volume of the hemisphere, we take half of the volume of the sphere. V_hemisphere = V_sphere / 2 = (20.833333...π m^3) / 2 = 10.416666...π m^3Perform Multiplication: Now, we approximate π as 3.14159 and perform the multiplication to find the numerical value of the volume. V_hemisphere ≈ 10.416666... × 3.14159 m^3Round Volume: Perform the multiplication to get the volume of the hemisphere. V_hemisphere ≈ 32.7249 m^3Finally, we round the volume to the nearest tenth of a cubic meter as asked in the question prompt. V_hemisphere ≈ 32.7 m^3

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Evaluate variable expressions: word problems

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

5 \mathrm{~m}

, rounded to the nearest tenth of a cubic meter?

\newline

Answer:

\mathrm{m}^{3}

Find Radius: First, we need to find the radius of the hemisphere. The radius is half of the diameter. $\newline$ Given diameter = $5\,\text{m}$ , so radius $r = \frac{\text{diameter}}{2} = \frac{5\,\text{m}}{2} = 2.5\,\text{m}$ .
Calculate Volume of Sphere: Next, we use the formula for the volume of a sphere, which is $V = \frac{4}{3}\pi r^3$ , and then we will take half of that volume to find the volume of the hemisphere since a hemisphere is half of a sphere.
Calculate Volume of Sphere: Now, we calculate the volume of the sphere using the radius we found. $V_{\text{sphere}} = \frac{4}{3}\pi(2.5\,\text{m})^3$
Take Half of Volume: Perform the calculation for the volume of the sphere. $\newline$ $V_{\text{sphere}} = \frac{4}{3}\pi(2.5\,\text{m})^3 = \frac{4}{3}\pi(15.625\,\text{m}^3) = 20.833333...\pi\,\text{m}^3$
Approximate Pi: Since we need the volume of the hemisphere, we take half of the volume of the sphere. $\newline$ $V_{\text{hemisphere}} = \frac{V_{\text{sphere}}}{2} = \frac{(20.833333...\pi \, \text{m}^3)}{2} = 10.416666...\pi \, \text{m}^3$
Perform Multiplication: Now, we approximate $\pi$ as $3.14159$ and perform the multiplication to find the numerical value of the volume. $\newline$ $V_{\text{hemisphere}} \approx 10.416666... \times 3.14159 \, \text{m}^3$
Round Volume: Perform the multiplication to get the volume of the hemisphere. $V_{\text{hemisphere}} \approx 32.7249 \, \text{m}^3$
Round Volume: Perform the multiplication to get the volume of the hemisphere. $\newline$ $V_{\text{hemisphere}} \approx 32.7249 \, \text{m}^3$ Finally, we round the volume to the nearest tenth of a cubic meter as asked in the question prompt. $\newline$ $V_{\text{hemisphere}} \approx 32.7 \, \text{m}^3$