Volume of a Prism Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Volume - Prism" with several problems involving finding the volume of prisms. Since I can't view images directly, I’ll help you solve the problems based on the text you provided and typical formats for such worksheets.

Let me analyze each problem one by one, assuming standard prism volume formulas:

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🔷 Volume of a Prism Formula:

$$
\text{Volume} = \text{Base Area} \times \text{Height}
$$

For rectangular prisms, the base is a rectangle:
$$
\text{Base Area} = \text{length} \times \text{width}
$$

For triangular prisms, the base is a triangle:
$$
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

For prisms with parallelogram bases, use:
$$
\text{Base Area} = \text{base} \times \text{height}
$$

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Now let’s go through the problems as described in your image.

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✔ Problem 45:

> The base of a prism is a parallelogram whose base and height are 19 inches and 17 inches respectively. The height of the prism is 6 inches.

We are given:
- Base of parallelogram = 19 in
- Height of parallelogram = 17 in
- Height of prism (depth) = 6 in

First, find the area of the base (parallelogram):
$$
\text{Base Area} = \text{base} \times \text{height} = 19 \times 17 = 323 \text{ in}^2
$$

Now, volume:
$$
\text{Volume} = \text{Base Area} \times \text{Prism Height} = 323 \times 6 = 1938 \text{ in}^3
$$

✔ Answer: 1938 cubic inches

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✔ Problem 46:

> The base of a prism is a trapezoid whose height is 12 yards. The parallel bases of the trapezoidal measure 10 yards and 8 yards. The height of the prism is 5 yards. Find its volume.

We are given:
- Height of trapezoid = 12 yd
- Bases of trapezoid = 10 yd and 8 yd
- Height of prism = 5 yd

First, find the area of the trapezoidal base:
$$
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} = \frac{1}{2} \times (10 + 8) \times 12 = \frac{1}{2} \times 18 \times 12 = 108 \text{ yd}^2
$$

Now, volume:
$$
\text{Volume} = \text{Base Area} \times \text{Prism Height} = 108 \times 5 = 540 \text{ yd}^3
$$

✔ Answer: 540 cubic yards

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🟨 Problems 41–44 (Likely Rectangular or Triangular Prisms):

Since no specific numbers were provided for these, but they are likely labeled diagrams, here’s how to solve them if you have dimensions:

#### Example (if it's a rectangular prism):
Suppose a box has length = 10 cm, width = 5 cm, height = 4 cm.
$$
\text{Volume} = 10 \times 5 \times 4 = 200 \text{ cm}^3
$$

#### Example (if it's a triangular prism):
Suppose base triangle has base = 6 cm, height = 4 cm, and prism height = 10 cm.
$$
\text{Base Area} = \frac{1}{2} \times 6 \times 4 = 12 \text{ cm}^2 \\
\text{Volume} = 12 \times 10 = 120 \text{ cm}^3
$$

👉 So for each shape, identify:
1. What kind of base it has (rectangle, triangle, etc.)
2. Measure or read the dimensions
3. Use the appropriate formula

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 45 | 1938 in³ |
| 46 | 540 yd³ |

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If you can provide the dimensions for problems 41–44 (e.g., "length = 8 cm, width = 5 cm, height = 3 cm"), I can compute those too!

Let me know if you'd like step-by-step solutions for any other shapes or need help interpreting the diagrams.