Sure! Let’s solve each problem step by step. The worksheet asks for the
volume of each figure to the nearest tenth, and you’re told to use
π = 3.14.
We’ll identify the shape, recall the volume formula, plug in the numbers, and round to the nearest tenth.
---
1. Triangular Prism
- Base: Triangle with base = 22 in., height = 22 in.
- Length (height of prism) = 42 in.
Formula:
Volume = Area of base × height of prism
Area of triangle = (1/2) × base × height = (1/2) × 22 × 22 = 242 in²
Volume = 242 × 42 =
10,164 in³
✔ Answer: 10,164.0 in³
---
2. Cylinder
- Radius = 6.5 cm
- Height = 16 cm
Formula:
V = πr²h = 3.14 × (6.5)² × 16
Calculate:
6.5² = 42.25
42.25 × 16 = 676
676 × 3.14 = 2122.64
✔ Answer: 2,122.6 cm³
---
3. Cube
- Side = 13 m
Formula:
V = side³ = 13 × 13 × 13 = 2197
✔ Answer: 2,197.0 m³
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4. Rectangular Prism
- Dimensions: 45 cm × 12 cm × 6 cm
Formula:
V = l × w × h = 45 × 12 × 6
45 × 12 = 540
540 × 6 = 3240
✔ Answer: 3,240.0 cm³
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5. Triangular Prism
- Triangle base: base = 18 m, height = 10 m
- Length of prism = 28 m
Area of triangle = (1/2) × 18 × 10 = 90 m²
Volume = 90 × 28 =
2,520 m³
✔ Answer: 2,520.0 m³
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6. Cylinder
- Diameter = 32 cm → radius = 16 cm
- Height = 15 cm
Formula:
V = πr²h = 3.14 × (16)² × 15
16² = 256
256 × 15 = 3840
3840 × 3.14 = 12,057.6
✔ Answer: 12,057.6 cm³
---
7. Rectangular Prism
- Dimensions: 11 in. × 17 in. × 31 in.
V = 11 × 17 × 31
11 × 17 = 187
187 × 31 = 5,797
✔ Answer: 5,797.0 in³
---
8. Triangular Prism
- Triangle base: base = 14 m, height = 14 m
- Length of prism = 27 m
Area of triangle = (1/2) × 14 × 14 = 98 m²
Volume = 98 × 27 =
2,646 m³
✔ Answer: 2,646.0 m³
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9. Cube
- Side = 14.3 ft
V = (14.3)³ = 14.3 × 14.3 × 14.3
First, 14.3 × 14.3 = 204.49
Then, 204.49 × 14.3
Let’s compute:
204.49 × 14 = 2862.86
204.49 × 0.3 = 61.347
Total = 2862.86 + 61.347 =
2924.207
Rounded to nearest tenth →
2,924.2 ft³
✔ Answer: 2,924.2 ft³
---
##
✔ Final Answers Summary:
1.
10,164.0 in³
2.
2,122.6 cm³
3.
2,197.0 m³
4.
3,240.0 cm³
5.
2,520.0 m³
6.
12,057.6 cm³
7.
5,797.0 in³
8.
2,646.0 m³
9.
2,924.2 ft³
Let me know if you’d like a diagram or explanation for any specific one!
Parent Tip: Review the logic above to help your child master the concept of volume of cylinders and prisms worksheet.
