Question

The volume of this cylinder is 492,452.48 cubic meters. What is the height?

Use ≈ 3.14 for pi and round your answer to the nearest hundredth. No height is given, but the radius is 52?

Answer 1

• Answer:

`\Large{\boxed{\sf Height = 58 \: m}}`

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• Step-by-step explanation:

The volume of a cylinder can be calculated using the following formula:

`\Large{\sf V = B * h}`

Where:

• V is the volume of the cylinder.
• B is the area of its base.
• h is the height of the cylinder.

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Since we are not given the area of its base, which is a circle, we will have to calculate it applying the following formula:

`\Large{\sf B = \pi * r^2}`

Where:

• B is the area of the circle (the base of the cylinder).
• r is its radius.

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Combining these two formulas, we can express the volume of the cylinder as follows:

`\Large{\sf V = \underbrace{\sf \pi * r^2}_(B) * h}`

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Now, rearrange the formula to isolate the height, h.

`\sf V = \pi * r^2 * h \Longleftrightarrow (V)/(\pi * * r^2) = ( \pi * r^2 * h)/(\pi * r^2 ) \Longleftrightarrow h = (V)/(\pi * r^2)`

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`\Large{\boxed{\sf Given \text{:} } \begin{cases} \sf V &=\sf 492,452.48 \: m^3 \\ \sf r &=\sf 52 \: m \: \\ \sf \pi &= \sf 3.14 \: (approximately) \end{cases} }`

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Substitute these values into our formula:

`\sf h = (492,452.48 \: m^3)/((52 \: m)^2 * 3.14 ) = (492,452.48 \: m^3)/(8,490.56\: m^2 ) \\ \\ \\ \\ \implies \boxed{\boxed{\sf h = 58 \: m}}`