What is the volume of a hemisphere with a radius of 29m, rounded to the nearest tenth of a cubic meter? Answer: m^(3)

Calculate Volume of Sphere Formula: The formula to calculate the volume of a sphere is V = (4/3)πr^3. Since we want the volume of a hemisphere, we need to divide the volume of a sphere by 2. Therefore, the formula for the volume of a hemisphere is V = (1/2)(4/3)πr^3.Plug in Radius: Let's plug in the radius (r = 29m) into the formula for the volume of a hemisphere: V = (1/2)(4/3)π(29)^3.Calculate Volume: Now, we calculate the volume: V = (1/2)(4/3)π(29)^3 = (2/3)π(29)^3 = (2/3)π(24389).Compute Numerical Value: We can now compute the numerical value: V = (2/3)π(24389) ≈ (2/3)(3.14159)(24389) ≈ 50965.21307 m^3.Round Volume: Finally, we round the volume to the nearest tenth of a cubic meter: V ≈ 50965.2 m^3.

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What is the volume of a hemisphere with a radius of
29m, rounded to the nearest tenth of a cubic meter?
Answer:
m^(3)

What is the volume of a hemisphere with a radius of $29 \mathrm{~m}$ , rounded to the nearest tenth of a cubic meter? $\newline$ Answer: $\mathrm{m}^{3}$

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Grade 7

Convert between customary and metric systems

Full solution

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

29 \mathrm{~m}

, rounded to the nearest tenth of a cubic meter?

\newline

Answer:

\mathrm{m}^{3}

Calculate Volume of Sphere Formula: The formula to calculate the volume of a sphere is $V = \frac{4}{3}\pi r^3$ . Since we want the volume of a hemisphere, we need to divide the volume of a sphere by $2$ . Therefore, the formula for the volume of a hemisphere is $V = \frac{1}{2}\left(\frac{4}{3}\pi r^3\right)$ .
Plug in Radius: Let's plug in the radius $r = 29\,\text{m}$ into the formula for the volume of a hemisphere: $V = \left(\frac{1}{2}\right)\left(\frac{4}{3}\right)\pi(29)^3$ .
Calculate Volume: Now, we calculate the volume: $V = (\frac{1}{2})(\frac{4}{3})\pi(29)^3 = (\frac{2}{3})\pi(29)^3 = (\frac{2}{3})\pi(24389)$ .
Compute Numerical Value: We can now compute the numerical value: $V = \frac{2}{3}\pi(24389) \approx \frac{2}{3}(3.14159)(24389) \approx 50965.21307 \, m^3$ .
Round Volume: Finally, we round the volume to the nearest tenth of a cubic meter: $V \approx 50965.2 \, \text{m}^3$ .