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\( -12 \mathrm{~cm} \) \( \qquad \) 4 9 cm You want to catch rainwater in this cylindrical container: About how much water will it hold?

Ask by Ross Frazier. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

The cylindrical container can hold approximately 452 cubic centimeters (cm³) of water.

Solution

To determine how much rainwater the cylindrical container can hold, we'll calculate its volume using the formula for the volume of a cylinder: \[ \text{Volume} = \pi r^2 h \] Where: - \( r \) is the radius of the cylinder. - \( h \) is the height of the cylinder. - \( \pi \) (pi) is approximately 3.14159. From the information provided: - It seems the cylinder has a **radius (\( r \)) of 4 cm**. - The **height (\( h \)) is 9 cm**. Using these values: \[ \text{Volume} = \pi \times (4\, \text{cm})^2 \times 9\, \text{cm} \] \[ \text{Volume} = \pi \times 16\, \text{cm}^2 \times 9\, \text{cm} \] \[ \text{Volume} = 144\pi\, \text{cm}^3 \] \[ \text{Volume} \approx 144 \times 3.14159\, \text{cm}^3 \] \[ \text{Volume} \approx 452.39\, \text{cm}^3 \] **Conclusion:** The cylindrical container can hold approximately **452 cubic centimeters (cm³)** of water. Since 1 liter is equivalent to 1,000 cm³, this is also about **0.452 liters** of water.

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To calculate the volume of a cylindrical container, you can use the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Given that the height is \( -12 \) cm (assuming it's a typo since height cannot be negative) and the diameter is \( 9 \) cm, the radius \( r \) would be \( 4.5 \) cm. Plugging these values into the formula, if we assume the height is actually \( 12 \) cm, the volume would be: \[ V = \pi (4.5^2)(12) \approx 254.47 \text{ cm}^3. \] So, your cylindrical container would hold approximately \( 254.47 \) cm³ of rainwater! Imagining rainwater collected over a lovely afternoon? With about 254.47 cm³ of space in your cylindrical container, that's enough to fill up a small cup! Who knew rainwater could be so entertaining? Just think of all the little adventures you could have tracking how full your container gets with each passing shower. What about using that water to start a tiny indoor garden? 🌧️🌱

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