Calculate the Volume of Cones Worksheet

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

The formula for the volume of a cone is:

Volume = (1/3) × π × r² × h

Where:
- r = radius of the base
- h = height of the cone
- We’ll use π ≈ 3.14 unless told otherwise

---

Problem 1:

Radius = 3 cm, Height = 6 cm
V = (1/3) × 3.14 × (3)² × 6
= (1/3) × 3.14 × 9 × 6
First: 9 × 6 = 54
Then: 54 × 3.14 = 169.56
Then: 169.56 ÷ 3 = 56.52 cm³

✔ Check: 3²=9, 9×6=54, 54×3.14=169.56, ÷3=56.52 → Correct

---

Problem 2:

Radius = 4 ft, Height = 8 ft
V = (1/3) × 3.14 × (4)² × 8
= (1/3) × 3.14 × 16 × 8
First: 16 × 8 = 128
Then: 128 × 3.14 = 401.92
Then: 401.92 ÷ 3 ≈ 133.97 ft³

✔ Check: 4²=16, 16×8=128, 128×3.14=401.92, ÷3≈133.97 → Correct

---

Problem 3:

Radius = 2 ft, Height = 8 ft
V = (1/3) × 3.14 × (2)² × 8
= (1/3) × 3.14 × 4 × 8
First: 4 × 8 = 32
Then: 32 × 3.14 = 100.48
Then: 100.48 ÷ 3 ≈ 33.49 ft³

✔ Check: 2²=4, 4×8=32, 32×3.14=100.48, ÷3≈33.49 → Correct

---

Problem 4:

Radius = 4 ft, Height = 8 ft → Same as #2!
So answer is also 133.97 ft³

Wait — let me double-check the image description… Actually, in your original list, #4 has same dimensions as #2? Let me recheck based on standard worksheet patterns.

Actually, looking back at your input:

Problem 4 says: “8 ft” height and “4 ft” radius — yes, same as #2. So same answer.

But wait — maybe I misread? Let me check again from your text:

You wrote:

> 4. [cone] 8 ft (height), 4 ft (radius)

Yes — so same as #2.

BUT — hold on! In many worksheets, sometimes they switch numbers. Let me be sure.

Actually, no — according to your typed list:

#2: 8 ft height, 4 ft radius
#4: 8 ft height, 4 ft radius → identical

So yes, same answer: 133.97 ft³

But let’s recalculate just to be safe:

(1/3) × 3.14 × 16 × 8 = same as before → 133.97 → OK

---

Problem 5:

Radius = 4 ft, Height = 6 ft
V = (1/3) × 3.14 × (4)² × 6
= (1/3) × 3.14 × 16 × 6
First: 16 × 6 = 96
Then: 96 × 3.14 = 301.44
Then: 301.44 ÷ 3 = 100.48 ft³

✔ Check: 4²=16, 16×6=96, 96×3.14=301.44, ÷3=100.48 → Correct

---

Problem 6:

Radius = 6 cm, Height = 6 cm
V = (1/3) × 3.14 × (6)² × 6
= (1/3) × 3.14 × 36 × 6
First: 36 × 6 = 216
Then: 216 × 3.14 = 678.24
Then: 678.24 ÷ 3 = 226.08 cm³

✔ Check: 6²=36, 36×6=216, 216×3.14=678.24, ÷3=226.08 → Correct

---

Now, compiling all answers:

1. 56.52 cm³
2. 133.97 ft³
3. 33.49 ft³
4. 133.97 ft³
5. 100.48 ft³
6. 226.08 cm³

Note: Units are important — keep them as given (cm or ft).

Final Answer:
1. 56.52 cm³
2. 133.97 ft³
3. 33.49 ft³
4. 133.97 ft³
5. 100.48 ft³
6. 226.08 cm³