Volume Word Problems Worksheet - Free Printable

Let's solve each problem step by step using the volume formulas provided.

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Problem 1: Farmer Zeke's Grain Silo

Given:
- The silo is a cylinder
- Radius $ r = 45 $ feet
- Height $ h = 135 $ feet

Formula for volume of a cylinder:
$$
V = \pi r^2 h
$$

Plug in the values:
$$
V = \pi (45)^2 (135)
$$
$$
V = \pi (2025)(135)
$$
$$
V = \pi (273,375)
$$
$$
V \approx 3.1416 \times 273,375 \approx 858,543.75 \text{ cubic feet}
$$

✔ Answer: The volume of the grain silo is approximately 858,544 cubic feet.

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Problem 2: Kyle’s Chocolate Pyramid

Given:
- A rectangular pyramid
- Base: $ l = 6 $ inches, $ w = 6 $ inches
- Height $ h = 9 $ inches

Formula for volume of a rectangular pyramid:
$$
V = \frac{l \cdot w \cdot h}{3}
$$

Plug in the values:
$$
V = \frac{6 \cdot 6 \cdot 9}{3} = \frac{324}{3} = 108
$$

✔ Answer: The volume of the pyramid is 108 cubic inches.

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Problem 3: Marshmallow Peeps Package

Given:
- A rectangular prism
- Length $ l = 8 $ inches
- Width $ w = 10 $ inches
- Height $ h = 3 $ inches

Formula for volume of a rectangular prism:
$$
V = l \cdot w \cdot h
$$

$$
V = 8 \cdot 10 \cdot 3 = 240
$$

✔ Answer: The volume of the package is 240 cubic inches.

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Problem 4: Perfect Ice Cube

Given:
- A cube
- Side length $ a = 22 $ mm

Formula for volume of a cube:
$$
V = a^3
$$

$$
V = 22^3 = 22 \cdot 22 \cdot 22 = 484 \cdot 22 = 10,648
$$

✔ Answer: The volume of the ice cube is 10,648 cubic millimeters.

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Problem 5: Timmy’s Wall

Given:
- Timmy used 6 cubes, each with side $ = 14 $ cm
- He arranged them into a $ 2 \times 3 $ wall

We need to find the total volume of the wall.

Each cube has volume:
$$
V_{\text{cube}} = 14^3 = 14 \cdot 14 \cdot 14 = 196 \cdot 14 = 2,744 \text{ cm}^3
$$

Total volume of 6 cubes:
$$
V_{\text{total}} = 6 \cdot 2,744 = 16,464 \text{ cm}^3
$$

Alternatively, we can think of the wall as a larger rectangular prism:
- Since it's a $ 2 \times 3 $ wall, and each cube is 14 cm on a side:
- Length: $ 3 \times 14 = 42 $ cm
- Width: $ 2 \times 14 = 28 $ cm
- Height: $ 14 $ cm (since only one layer high)

So,
$$
V = 42 \cdot 28 \cdot 14 = (42 \cdot 28) \cdot 14 = 1,176 \cdot 14 = 16,464 \text{ cm}^3
$$

✔ Answer: The volume of Timmy’s wall is 16,464 cubic centimeters.

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✔ Final Answers:

1. 858,544 ft³
2. 108 in³
3. 240 in³
4. 10,648 mm³
5. 16,464 cm³

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