Math worksheet for calculating the volume of various 3D shapes including prisms, pyramids, cylinders, and cones.

Here is the step-by-step solution for each figure, using the appropriate volume formulas and rounding to the nearest hundredth where necessary.

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1) Cylinder

- Formula: \( V = \pi r^2 h \)
- Radius \( r = 7 \) yd, Height \( h = 10 \) yd
- \( V = \pi \cdot 7^2 \cdot 10 = \pi \cdot 49 \cdot 10 = 490\pi \)
- \( V \approx 490 \cdot 3.1416 = 1539.38 \) yd³

✔ Answer: 1539.38 yd³

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2) Rectangular Prism

- Formula: \( V = l \cdot w \cdot h \)
- Length \( l = 14 \) in, Width \( w = 6 \) in, Height \( h = 8 \) in
- \( V = 14 \cdot 6 \cdot 8 = 672 \) in³

✔ Answer: 672.00 in³

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3) Cube

- Formula: \( V = s^3 \)
- Side \( s = 6 \) yd
- \( V = 6^3 = 216 \) yd³

✔ Answer: 216.00 yd³

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4) Square Pyramid

- Formula: \( V = \frac{1}{3} \cdot B \cdot h \), where \( B \) is base area
- Base is square: side = 11 ft → \( B = 11 \cdot 11 = 121 \) ft²
- Height \( h = 13 \) ft (given as slant height? Wait — check image)

⚠️ Important Note: The 13 ft is labeled as the *slant height*, not the vertical height. We need the vertical height to compute volume.

But wait — looking at the diagram, the 13 ft is drawn from apex to base center, perpendicular to base — so it is the vertical height. The right angle symbol confirms it’s perpendicular.

So:
- \( V = \frac{1}{3} \cdot 121 \cdot 13 = \frac{1573}{3} \approx 524.33 \) ft³

✔ Answer: 524.33 ft³

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5) Triangular Prism

- Formula: \( V = \text{Base Area} \cdot \text{Height} \)
- Base is triangle: base = 8 mm, height = 6 mm → Area = \( \frac{1}{2} \cdot 8 \cdot 6 = 24 \) mm²
- Prism height (length) = 14 mm
- \( V = 24 \cdot 14 = 336 \) mm³

✔ Answer: 336.00 mm³

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6) Triangular Prism (equilateral base?)

- Base is a triangle with base = 6 in, height = 6 in? Wait — diagram shows base triangle with two sides labeled 6 in, and prism height 12 in.

Actually, the base is a right triangle? Looking at the drawing: it appears to be an isosceles right triangle with legs 6 in each? Or maybe equilateral?

Wait — the base triangle has base 6 in and height 6 in (perpendicular height shown). So:

- Base area = \( \frac{1}{2} \cdot 6 \cdot 6 = 18 \) in²
- Prism length (height) = 12 in
- \( V = 18 \cdot 12 = 216 \) in³

✔ Answer: 216.00 in³

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7) Cone

- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Radius \( r = 3 \) cm, Height \( h = 11 \) cm
- \( V = \frac{1}{3} \pi \cdot 3^2 \cdot 11 = \frac{1}{3} \pi \cdot 9 \cdot 11 = 33\pi \)
- \( V \approx 33 \cdot 3.1416 = 103.67 \) cm³

✔ Answer: 103.67 cm³

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8) Square Pyramid

- Formula: \( V = \frac{1}{3} \cdot B \cdot h \)
- Base is square: side = 14 ft → \( B = 14 \cdot 14 = 196 \) ft²
- Height \( h = 10.954 \) ft (given as vertical height — confirmed by diagram)
- \( V = \frac{1}{3} \cdot 196 \cdot 10.954 \)

Calculate:
- \( 196 \cdot 10.954 = 2146.984 \)
- \( \frac{2146.984}{3} \approx 715.66 \) ft³

✔ Answer: 715.66 ft³

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9) Cone

- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Diameter = 8 mm → radius \( r = 4 \) mm
- Height \( h = 14 \) mm
- \( V = \frac{1}{3} \pi \cdot 4^2 \cdot 14 = \frac{1}{3} \pi \cdot 16 \cdot 14 = \frac{224}{3} \pi \)
- \( \frac{224}{3} \approx 74.6667 \)
- \( 74.6667 \cdot \pi \approx 74.6667 \cdot 3.1416 \approx 234.57 \) mm³

✔ Answer: 234.57 mm³

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## ✔ Final Answers:

1) 1539.38 yd³
2) 672.00 in³
3) 216.00 yd³
4) 524.33 ft³
5) 336.00 mm³
6) 216.00 in³
7) 103.67 cm³
8) 715.66 ft³
9) 234.57 mm³

Let me know if you’d like diagrams or formula reminders!