Math worksheet for calculating the volume of cones using the formula with given dimensions.

Let’s solve each cone volume problem step by step.
We’ll use the formula for the volume of a cone:
Volume = (1/3) × B × h, where B = area of the base = π × r², and we’re told to use π = 3.14.

Also remember:
- Radius (r) is half the diameter.
- Height (h) is the perpendicular distance from the base to the tip.
- The “slant height” (the diagonal side) is NOT the height — only use it if you need to find radius or height using Pythagoras, but in these problems, they give us what we need directly.

---

Problem 1:

Figure shows:
- Height (h) = 3 in
- Radius (r) = 2 in (since it’s labeled from center to edge)

So:
Radius = 2 in
Diameter = 2 × 2 = 4 in
B = π × r² = 3.14 × 2² = 3.14 × 4 = 12.56 in²
h = 3 in
Volume = (1/3) × 12.56 × 3 = 12.56 in³ → because (1/3)×3 cancels out.

✔ Volume = 12.56 in³

---

Problem 2:

Figure shows:
- Slant height = 7 in (diagonal)
- Radius = 2 in (from center to edge on base)
But wait — we need the vertical height (h), not slant height!

Use Pythagorean theorem:
In a right triangle formed by radius, height, and slant height:
r² + h² = slant²
→ 2² + h² = 7²
→ 4 + h² = 49
→ h² = 45
→ h = √45 ≈ 6.708 in

Now calculate:
Radius = 2 in
Diameter = 4 in
B = 3.14 × 2² = 12.56 in²
h ≈ 6.708 in
Volume = (1/3) × 12.56 × 6.708 ≈ (1/3) × 84.25 ≈ 28.08 in³

Wait — let me double-check that multiplication:
12.56 × 6.708 = let’s compute:

12.56 × 6 = 75.36
12.56 × 0.7 = 8.792
12.56 × 0.008 = 0.10048
Total ≈ 75.36 + 8.792 = 84.152 + 0.10048 ≈ 84.25248
Divide by 3: 84.25248 ÷ 3 ≈ 28.084 → round to 28.08 in³

✔ Volume ≈ 28.08 in³

---

Problem 3:

Figure shows:
- Radius = 3 in (labeled from center to edge)
- Height = 5 in (vertical line from base to tip)

So:
Radius = 3 in
Diameter = 6 in
B = 3.14 × 3² = 3.14 × 9 = 28.26 in²
h = 5 in
Volume = (1/3) × 28.26 × 5 = (1/3) × 141.3 = 47.1 in³

✔ Volume = 47.1 in³

---

Problem 4:

Figure shows:
- Diameter = 8 in → so Radius = 4 in
- Height = 6 in

Radius = 4 in
Diameter = 8 in
B = 3.14 × 4² = 3.14 × 16 = 50.24 in²
h = 6 in
Volume = (1/3) × 50.24 × 6 = (1/3) × 301.44 = 100.48 in³

✔ Volume = 100.48 in³

---

Problem 5:

Figure shows:
- Slant height = 15 in
- Diameter = 10 in → so Radius = 5 in

Again, we need vertical height (h). Use Pythagoras:
r² + h² = slant²
→ 5² + h² = 15²
→ 25 + h² = 225
→ h² = 200
→ h = √200 ≈ 14.142 in

Now:
Radius = 5 in
Diameter = 10 in
B = 3.14 × 5² = 3.14 × 25 = 78.5 in²
h ≈ 14.142 in
Volume = (1/3) × 78.5 × 14.142 ≈ (1/3) × 1110.147 ≈ 370.05 in³

Check: 78.5 × 14.142
78.5 × 14 = 1099
78.5 × 0.142 ≈ 11.147
Total ≈ 1110.147 → divide by 3 → 370.049 → round to 370.05 in³

✔ Volume ≈ 370.05 in³

---

Problem 6:

Figure shows:
- Slant height = 6 in
- Radius = 4 in? Wait — look again.

Actually, the figure labels:
One leg is 4 in (probably height?), other leg is unknown, hypotenuse is 6 in.

Wait — re-examining: It looks like the 4 in is the radius (from center to edge), and 6 in is the slant height.

So same as before:
r = 4 in, slant = 6 in → find h.

Pythagoras:
r² + h² = slant²
→ 4² + h² = 6²
→ 16 + h² = 36
→ h² = 20
→ h = √20 ≈ 4.472 in

Now:
Radius = 4 in
Diameter = 8 in
B = 3.14 × 4² = 3.14 × 16 = 50.24 in²
h ≈ 4.472 in
Volume = (1/3) × 50.24 × 4.472 ≈ (1/3) × 224.673 ≈ 74.89 in³

Check: 50.24 × 4.472
50.24 × 4 = 200.96
50.24 × 0.4 = 20.096
50.24 × 0.07 = 3.5168
50.24 × 0.002 = 0.10048
Add: 200.96 + 20.096 = 221.056 + 3.5168 = 224.5728 + 0.10048 ≈ 224.673
÷3 → 74.891 → round to 74.89 in³

✔ Volume ≈ 74.89 in³

---

Final Answer:

1. Radius: 2 in, Diameter: 4 in, B: 12.56 in², h: 3 in, Volume: 12.56 in³
2. Radius: 2 in, Diameter: 4 in, B: 12.56 in², h: ~6.71 in, Volume: ~28.08 in³
3. Radius: 3 in, Diameter: 6 in, B: 28.26 in², h: 5 in, Volume: 47.1 in³
4. Radius: 4 in, Diameter: 8 in, B: 50.24 in², h: 6 in, Volume: 100.48 in³
5. Radius: 5 in, Diameter: 10 in, B: 78.5 in², h: ~14.14 in, Volume: ~370.05 in³
6. Radius: 4 in, Diameter: 8 in, B: 50.24 in², h: ~4.47 in, Volume: ~74.89 in³