Volume of a Cone worksheet with diagrams and problems for calculating cone volume.

Let’s solve each cone volume problem step by step.

We are told to use π = 3.14
The formula for the volume of a cone is:
V = (1/3) × π × r² × h

Where:
- r = radius of the base
- h = height of the cone (perpendicular from base to tip)

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Problem 2:

Given:
Radius r = 5 m
Height h = 7 m

V = (1/3) × 3.14 × (5)² × 7
= (1/3) × 3.14 × 25 × 7
First, 25 × 7 = 175
Then, 3.14 × 175 = 549.5
Then, 549.5 ÷ 3 = 183.166... → round to two decimals? Let’s keep as is or check if needed.

Actually, let’s compute precisely:

3.14 × 25 = 78.5
78.5 × 7 = 549.5
549.5 ÷ 3 = 183.166... ≈ 183.17 m³

But since problem 1 gave answer with two decimals, we’ll do same.

✔ V = 183.17 m³

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Problem 3:

Given:
Radius r = 2 mm
Height h = 4 mm

V = (1/3) × 3.14 × (2)² × 4
= (1/3) × 3.14 × 4 × 4
Wait — 2² = 4, then × 4 = 16? No:

(2)² = 4
Then 4 × 4 = 16? Wait no — it’s r² × h = 4 × 4 = 16? Actually:

r² = 4
h = 4
So r² × h = 4 × 4 = 16

Then:
V = (1/3) × 3.14 × 16
= (1/3) × 50.24
= 50.24 ÷ 3 = 16.746... ≈ 16.75 mm³

✔ V = 16.75 mm³

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Problem 4:

Given:
Radius r = 10 cm
Height h = 7 cm

V = (1/3) × 3.14 × (10)² × 7
= (1/3) × 3.14 × 100 × 7
= (1/3) × 3.14 × 700
= (1/3) × 2198
= 2198 ÷ 3 = 732.666... ≈ 732.67 cm³

✔ V = 732.67 cm³

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Problem 5:

Given:
Radius r = 4 m
Height h = 12 m

V = (1/3) × 3.14 × (4)² × 12
= (1/3) × 3.14 × 16 × 12
First, 16 × 12 = 192
Then, 3.14 × 192 = let’s calculate:

3 × 192 = 576
0.14 × 192 = 26.88
Total = 576 + 26.88 = 602.88
Then divide by 3: 602.88 ÷ 3 = 200.96

✔ V = 200.96 m³

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Problem 6:

Given:
Diameter = 12 mm → so radius r = 6 mm
Height h = 13 mm

V = (1/3) × 3.14 × (6)² × 13
= (1/3) × 3.14 × 36 × 13
First, 36 × 13 = 468
Then, 3.14 × 468 = ?

3 × 468 = 1404
0.14 × 468 = 65.52
Total = 1404 + 65.52 = 1469.52
Divide by 3: 1469.52 ÷ 3 = 489.84

✔ V = 489.84 mm³

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Problem 7:

Given:
Radius r = 8 cm
Height h = 13 cm

V = (1/3) × 3.14 × (8)² × 13
= (1/3) × 3.14 × 64 × 13
First, 64 × 13 = 832
Then, 3.14 × 832 = ?

3 × 832 = 2496
0.14 × 832 = 116.48
Total = 2496 + 116.48 = 2612.48
Divide by 3: 2612.48 ÷ 3 = 870.826... ≈ 870.83 cm³

✔ V = 870.83 cm³

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Problem 8:

Given:
Radius r = 5 m
Height h = 15 m

V = (1/3) × 3.14 × (5)² × 15
= (1/3) × 3.14 × 25 × 15
First, 25 × 15 = 375
Then, 3.14 × 375 = ?

3 × 375 = 1125
0.14 × 375 = 52.5
Total = 1125 + 52.5 = 1177.5
Divide by 3: 1177.5 ÷ 3 = 392.5

✔ V = 392.50 m³ (we can write as 392.5, but to match format, maybe 392.50)

Actually, 392.5 is fine, but let’s write as 392.50 to be consistent with two decimals.

✔ V = 392.50 m³

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Problem 9:

Given:
Radius r = 9 m
Height h = 14 m

V = (1/3) × 3.14 × (9)² × 14
= (1/3) × 3.14 × 81 × 14
First, 81 × 14 = 1134
Then, 3.14 × 1134 = ?

3 × 1134 = 3402
0.14 × 1134 = 158.76
Total = 3402 + 158.76 = 3560.76
Divide by 3: 3560.76 ÷ 3 = 1186.92

✔ V = 1186.92 m³

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Problem 10:

Given:
Radius r = 2 mm
Height h = 13 mm

V = (1/3) × 3.14 × (2)² × 13
= (1/3) × 3.14 × 4 × 13
First, 4 × 13 = 52
Then, 3.14 × 52 = ?

3 × 52 = 156
0.14 × 52 = 7.28
Total = 156 + 7.28 = 163.28
Divide by 3: 163.28 ÷ 3 = 54.426... ≈ 54.43 mm³

✔ V = 54.43 mm³

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Final Answer:

2) 183.17 m³
3) 16.75 mm³
4) 732.67 cm³
5) 200.96 m³
6) 489.84 mm³
7) 870.83 cm³
8) 392.50 m³
9) 1186.92 m³
10) 54.43 mm³