What is the volume of a hemisphere with a diameter of 51.2ft, rounded to the nearest tenth of a cubic foot? Answer: ft^(3)

Identify Radius: Identify the radius of the hemisphere. The diameter of the hemisphere is 51.2 feet. The radius is half of the diameter. Radius = Diameter / 2 Radius = 51.2 ft / 2 Radius = 25.6 ftWrite Volume Formula: Write down the formula for the volume of a sphere. The volume of a sphere is given by the formula: Volume of a sphere = (4/3) * π * r^3 Since we want the volume of a hemisphere (half of a sphere), we need to divide this by 2. Volume of a hemisphere = ((4/3) * π * r^3) / 2Substitute Radius: Substitute the radius into the formula for the volume of a hemisphere. Volume of a hemisphere = ((4/3) * π * (25.6 ft)^3) / 2Calculate Volume: Calculate the volume of the hemisphere. Volume of a hemisphere = ((4/3) * π * (25.6 ft)^3) / 2 Volume of a hemisphere = ((4/3) * π * 16777.216 ft^3) / 2 Volume of a hemisphere = (4 * π * 16777.216 ft^3) / 6 Volume of a hemisphere = (4 * π * 16777.216 ft^3) / 6 Volume of a hemisphere ≈ (4 * 3.14159 * 16777.216 ft^3) / 6 Volume of a hemisphere ≈ (4 * 3.14159 * 16777.216 ft^3) / 6 Volume of a hemisphere ≈ 223,256.7 ft^3 / 6 Volume of a hemisphere ≈ 37,209.45 ft^3Round Volume: Round the volume to the nearest tenth of a cubic foot. Volume of a hemisphere ≈ 37,209.5 ft^3 (rounded to the nearest tenth)

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What is the volume of a hemisphere with a diameter of
51.2ft, rounded to the nearest tenth of a cubic foot?
Answer:
ft^(3)

What is the volume of a hemisphere with a diameter of $51.2 \mathrm{ft}$ , rounded to the nearest tenth of a cubic foot? $\newline$ Answer: $\mathrm{ft}^{3}$

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Math Problems

Grade 6

Volume of cubes and rectangular prisms: word problems

Full solution

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

51.2 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

Answer:

\mathrm{ft}^{3}

Identify Radius: Identify the radius of the hemisphere. $\newline$ The diameter of the hemisphere is $51.2$ feet. The radius is half of the diameter. $\newline$ Radius $=$ Diameter $/$ $2$ $\newline$ Radius $=$ $51.2$ ft $/$ $2$ $\newline$ Radius $=$ $25.6$ ft
Write Volume Formula: Write down the formula for the volume of a sphere. $\newline$ The volume of a sphere is given by the formula: $\newline$ Volume of a sphere = $(\frac{4}{3}) \pi r^3$ $\newline$ Since we want the volume of a hemisphere (half of a sphere), we need to divide this by $2$ . $\newline$ Volume of a hemisphere = $\frac{(\frac{4}{3}) \pi r^3}{2}$
Substitute Radius: Substitute the radius into the formula for the volume of a hemisphere. Volume of a hemisphere = $\left(\frac{4}{3} \cdot \pi \cdot (25.6 \, \text{ft})^3\right) / 2$
Calculate Volume: Calculate the volume of the hemisphere. $\newline$ Volume of a hemisphere = $((4/3) * \pi * (25.6 \text{ ft})^3) / 2$ $\newline$ Volume of a hemisphere = $((4/3) * \pi * 16777.216 \text{ ft}^3) / 2$ $\newline$ Volume of a hemisphere = $(4 * \pi * 16777.216 \text{ ft}^3) / 6$ $\newline$ Volume of a hemisphere = $(4 * \pi * 16777.216 \text{ ft}^3) / 6$ $\newline$ Volume of a hemisphere $\approx (4 * 3.14159 * 16777.216 \text{ ft}^3) / 6$ $\newline$ Volume of a hemisphere $\approx (4 * 3.14159 * 16777.216 \text{ ft}^3) / 6$ $\newline$ Volume of a hemisphere $\approx 223,256.7 \text{ ft}^3 / 6$ $\newline$ Volume of a hemisphere $\approx 37,209.45 \text{ ft}^3$
Round Volume: Round the volume to the nearest tenth of a cubic foot. $\newline$ Volume of a hemisphere $\approx 37,209.5 \text{ ft}^3$ (rounded to the nearest tenth)