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What is the volume of a cylinder with a height of
9.9m and a base with a diameter of
5.2m, to the nearest tenth of a cubic meter?
Answer:
m^(3)

What is the volume of a cylinder with a height of $9.9 \mathrm{~m}$ and a base with a diameter of $5.2 \mathrm{~m}$ , to the nearest tenth of a cubic meter? $\newline$ Answer: $\mathrm{m}^{3}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. What is the volume of a cylinder with a height of

9.9 \mathrm{~m}

and a base with a diameter of

5.2 \mathrm{~m}

, to the nearest tenth of a cubic meter?

\newline

Answer:

\mathrm{m}^{3}

Identify formula for volume: Identify the formula for the volume of a cylinder. The formula for the volume of a cylinder is $V = \pi r^2 h$ , where $r$ is the radius of the base and $h$ is the height of the cylinder.
Calculate base radius: Calculate the radius of the base of the cylinder. $\newline$ The diameter of the base is given as $5.2$ meters. The radius is half of the diameter, so $r = \frac{\text{diameter}}{2} = \frac{5.2\,\text{m}}{2} = 2.6\,\text{m}$ .
Substitute radius and height: Substitute the radius and height into the volume formula. $\newline$ Using the radius of $2.6$ meters and the height of $9.9$ meters, the volume $V$ is calculated as $V = \pi \times (2.6\,\text{m})^2 \times 9.9\,\text{m}$ .
Perform volume calculation: Perform the calculation for the volume. $V = \pi \times (2.6\,\text{m})^2 \times 9.9\,\text{m} = \pi \times 6.76\,\text{m}^2 \times 9.9\,\text{m} \approx 3.14159 \times 6.76\,\text{m}^2 \times 9.9\,\text{m}.$
Complete final rounding: Complete the calculation and round to the nearest tenth. $\newline$ $V \approx 3.14159 \times 6.76 \times 9.9 \approx 209.937\,\text{m}^3$ . $\newline$ When rounded to the nearest tenth, the volume is approximately $209.9\,\text{m}^3$ .

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