Volume Word Problems worksheet with exercises on calculating volumes of cylinders, rectangular prisms, and other shapes.

Thank you for uploading the image. It contains a worksheet titled “Volume Word Problems” with 10 exercises involving calculating volumes of various 3D shapes — cylinders, rectangular prisms, spheres, and cones — in real-world contexts like water bottles, dumbbells, soccer balls, etc.

I’ll solve each problem step-by-step and explain the solution clearly.

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🔢 Key Volume Formulas Used:

- Cylinder: \( V = \pi r^2 h \)
- Rectangular Prism: \( V = l \times w \times h \)
- Sphere: \( V = \frac{4}{3} \pi r^3 \)
- Cone: \( V = \frac{1}{3} \pi r^2 h \)

*(Use \( \pi \approx 3.14 \) unless otherwise specified)*

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## ✔ Problem 1:
> A gym has a cylindrical water bottle with a radius of 5 centimeters and a height of 20 centimeters. Calculate the volume of water the bottle can hold in cubic centimeters.

Solution:
\[
V = \pi r^2 h = 3.14 \times 5^2 \times 20 = 3.14 \times 25 \times 20 = 3.14 \times 500 = 1570
\]

✔ Answer: 1570 cm³

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## ✔ Problem 2:
> A fitness enthusiast is using a rectangular dumbbell with dimensions 15 inches by 5 inches by 3 inches. Determine the volume of the dumbbell in cubic inches.

Solution:
\[
V = l \times w \times h = 15 \times 5 \times 3 = 225
\]

✔ Answer: 225 in³

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## ✔ Problem 3:
> A gym locker is shaped like a rectangular prism with dimensions 12 inches by 15 inches by 18 inches. Calculate the volume of the locker in cubic inches.

Solution:
\[
V = 12 \times 15 \times 18 = 180 \times 18 = 3240
\]

✔ Answer: 3240 in³

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## ✔ Problem 4:
> A soccer ball has a spherical shape with a radius of 11 centimeters. Determine the volume of the soccer ball in cubic centimeters.

Solution:
\[
V = \frac{4}{3} \pi r^3 = \frac{4}{3} \times 3.14 \times 11^3 = \frac{4}{3} \times 3.14 \times 1331
\]
First, \( 3.14 \times 1331 = 4179.34 \)
Then, \( \frac{4}{3} \times 4179.34 = \frac{16717.36}{3} ≈ 5572.45 \)

✔ Answer: ≈ 5572.45 cm³ (or 5572 cm³ if rounded to nearest whole number)

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## ✔ Problem 5:
> A swimmer is using a cylindrical buoy with a radius of 3 feet and a height of 4 feet. Calculate the volume of the buoy in cubic feet.

Solution:
\[
V = \pi r^2 h = 3.14 \times 3^2 \times 4 = 3.14 \times 9 \times 4 = 3.14 \times 36 = 113.04
\]

✔ Answer: 113.04 ft³

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## ✔ Problem 6:
> A runner is filling a conical water bottle with a radius of 6 centimeters and a height of 12 centimeters. Determine the volume of water the bottle can hold in cubic centimeters.

Solution:
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times 6^2 \times 12 = \frac{1}{3} \times 3.14 \times 36 \times 12
\]
First, \( 36 \times 12 = 432 \), then \( \frac{1}{3} \times 432 = 144 \), so:
\[
V = 3.14 \times 144 = 452.16
\]

✔ Answer: 452.16 cm³

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## ✔ Problem 7:
> A weightlifting plate is shaped like a circular cylinder with a radius of 8 inches and a thickness of 2 inches. Calculate the volume of the weightlifting plate in cubic inches.

*(Note: “Thickness” = height of cylinder)*

Solution:
\[
V = \pi r^2 h = 3.14 \times 8^2 \times 2 = 3.14 \times 64 \times 2 = 3.14 \times 128 = 401.92
\]

✔ Answer: 401.92 in³

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## ✔ Problem 8:
> A yoga mat is rolled into a cylindrical shape with a radius of 4 inches and a length of 72 inches. Determine the volume of the rolled-up yoga mat in cubic inches.

*(Length = height of cylinder)*

Solution:
\[
V = \pi r^2 h = 3.14 \times 4^2 \times 72 = 3.14 \times 16 \times 72
\]
First, \( 16 \times 72 = 1152 \), then \( 3.14 \times 1152 = 3617.28 \)

✔ Answer: 3617.28 in³

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## ✔ Problem 9:
> A weightlifting barbell is shaped like a cylindrical rod with a radius of 1 inch and a length of 72 inches. Determine the volume of the barbell in cubic inches.

*(Length = height)*

Solution:
\[
V = \pi r^2 h = 3.14 \times 1^2 \times 72 = 3.14 \times 72 = 226.08
\]

✔ Answer: 226.08 in³

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## ✔ Problem 10:
> A fitness room has a rectangular swimming pool with dimensions 20 meters by 10 meters by 2 meters. Determine the volume of the pool in cubic meters.

Solution:
\[
V = l \times w \times h = 20 \times 10 \times 2 = 400
\]

✔ Answer: 400 m³

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## 📝 Final Answers Summary:

1. 1570 cm³
2. 225 in³
3. 3240 in³
4. ≈5572.45 cm³
5. 113.04 ft³
6. 452.16 cm³
7. 401.92 in³
8. 3617.28 in³
9. 226.08 in³
10. 400 m³

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Let me know if you’d like these answers formatted as a worksheet answer key or need diagrams/explanations for any specific problem! 😊