Geometry Worksheets | Volume Worksheets - Free Printable

Explanation:
We need to find the volume of each cylinder and cone using their formulas:

- Volume of a cylinder:
$ V = \pi r^2 h $
where $ r $ is the radius, and $ h $ is the height.

- Volume of a cone:
$ V = \frac{1}{3} \pi r^2 h $

Important: Make sure you use radius, not diameter. If the diagram gives the diameter (the full width across), divide it by 2 to get the radius.

Let’s go one by one:

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1) Cylinder
Diameter = 7 yd → radius $ r = \frac{7}{2} = 3.5 $ yd
Height $ h = 10 $ yd
$ V = \pi (3.5)^2 (10) = \pi (12.25)(10) = 122.5\pi $
Using $ \pi \approx 3.1416 $:
$ V \approx 122.5 \times 3.1416 \approx 384.85 $
→ Rounded to nearest hundredth: 384.85 yd³

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2) Cone
Radius = 6 cm (given as radius — the line from center to edge)
Height = 14 cm
$ V = \frac{1}{3} \pi (6)^2 (14) = \frac{1}{3} \pi (36)(14) = \frac{1}{3} \pi (504) = 168\pi $
$ \approx 168 \times 3.1416 = 527.79 $
→ 527.79 cm³

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3) Cone
Diameter = 4 in → radius $ r = 2 $ in
Height = 11 in
$ V = \frac{1}{3} \pi (2)^2 (11) = \frac{1}{3} \pi (4)(11) = \frac{44}{3}\pi \approx 14.6667\pi $
$ \approx 14.6667 \times 3.1416 \approx 46.08 $
→ 46.08 in³

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4) Cylinder
Diameter = 8 yd → radius = 4 yd
Height = 12 yd
$ V = \pi (4)^2 (12) = \pi (16)(12) = 192\pi \approx 192 \times 3.1416 = 603.19 $
→ 603.19 yd³

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5) Cylinder
Diameter = 3 mm → radius = 1.5 mm
Height = 4 mm
$ V = \pi (1.5)^2 (4) = \pi (2.25)(4) = 9\pi \approx 9 \times 3.1416 = 28.27 $
→ 28.27 mm³

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6) Cylinder
Diameter = 4 in → radius = 2 in
Height = 6 in
$ V = \pi (2)^2 (6) = \pi (4)(6) = 24\pi \approx 24 \times 3.1416 = 75.40 $
→ 75.40 in³

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7) Cone
Diameter = 3 ft → radius = 1.5 ft
Height = 10 ft
$ V = \frac{1}{3} \pi (1.5)^2 (10) = \frac{1}{3} \pi (2.25)(10) = \frac{22.5}{3}\pi = 7.5\pi $
$ \approx 7.5 \times 3.1416 = 23.56 $
→ 23.56 ft³

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8) Cone
Radius = 6 ft (given as radius)
Height = 14 ft
$ V = \frac{1}{3} \pi (6)^2 (14) = \frac{1}{3} \pi (36)(14) = \frac{504}{3}\pi = 168\pi \approx 527.79 $
→ 527.79 ft³

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9) Cylinder
Radius = 3 cm (given as radius)
Height = 4 cm
$ V = \pi (3)^2 (4) = \pi (9)(4) = 36\pi \approx 36 \times 3.1416 = 113.10 $
→ 113.10 cm³

Double-check all calculations:

1) 3.5² = 12.25 × 10 = 122.5 × π ≈ 384.85 ✔
2) 6² = 36 × 14 = 504 ÷ 3 = 168 × π ≈ 527.79 ✔
3) 2² = 4 × 11 = 44 ÷ 3 = 14.6667 × π ≈ 46.08 ✔
4) 4² = 16 × 12 = 192 × π ≈ 603.19 ✔
5) 1.5² = 2.25 × 4 = 9 × π ≈ 28.27 ✔
6) 2² = 4 × 6 = 24 × π ≈ 75.40 ✔
7) 1.5² = 2.25 × 10 = 22.5 ÷ 3 = 7.5 × π ≈ 23.56 ✔
8) Same as #2 → 527.79 ✔
9) 3² = 9 × 4 = 36 × π ≈ 113.10 ✔

All correct.

Final Answer:
1) 384.85
2) 527.79
3) 46.08
4) 603.19
5) 28.27
6) 75.40
7) 23.56
8) 527.79
9) 113.10