Volume 2 - Free Printable

To solve the problem of finding the volume for each figure, we will use the appropriate volume formulas for each shape. Here are the formulas we will use:

1. Cone: \( V = \frac{1}{3} \pi r^2 h \)
2. Sphere: \( V = \frac{4}{3} \pi r^3 \)
3. Cylinder: \( V = \pi r^2 h \)
4. Hemisphere: \( V = \frac{2}{3} \pi r^3 \)

Let's calculate the volumes step by step for each figure.

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Figure 1: Cone

- Given: \( r = 21 \, \text{ft} \), \( h = 35 \, \text{ft} \)
- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Calculation:
\[
V = \frac{1}{3} \pi (21)^2 (35) = \frac{1}{3} \pi (441) (35) = \frac{1}{3} \pi (15435) = 5145 \pi \, \text{ft}^3
\]
- Volume: \( 5145 \pi \, \text{ft}^3 \)

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Figure 2: Sphere

- Given: \( r = 6 \, \text{in} \)
- Formula: \( V = \frac{4}{3} \pi r^3 \)
- Calculation:
\[
V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288 \pi \, \text{in}^3
\]
- Volume: \( 288 \pi \, \text{in}^3 \)

---

Figure 3: Cylinder

- Given: \( r = 4 \, \text{cm} \), \( h = 15 \, \text{cm} \)
- Formula: \( V = \pi r^2 h \)
- Calculation:
\[
V = \pi (4)^2 (15) = \pi (16) (15) = 240 \pi \, \text{cm}^3
\]
- Volume: \( 240 \pi \, \text{cm}^3 \)

---

Figure 4: Hemisphere

- Given: \( r = 9 \, \text{m} \)
- Formula: \( V = \frac{2}{3} \pi r^3 \)
- Calculation:
\[
V = \frac{2}{3} \pi (9)^3 = \frac{2}{3} \pi (729) = 486 \pi \, \text{m}^3
\]
- Volume: \( 486 \pi \, \text{m}^3 \)

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Figure 5: Cone

- Given: \( r = 24 \, \text{in} \), \( h = 50 \, \text{in} \)
- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Calculation:
\[
V = \frac{1}{3} \pi (24)^2 (50) = \frac{1}{3} \pi (576) (50) = \frac{1}{3} \pi (28800) = 9600 \pi \, \text{in}^3
\]
- Volume: \( 9600 \pi \, \text{in}^3 \)

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Figure 6: Sphere

- Given: \( r = 3 \, \text{mm} \)
- Formula: \( V = \frac{4}{3} \pi r^3 \)
- Calculation:
\[
V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36 \pi \, \text{mm}^3
\]
- Volume: \( 36 \pi \, \text{mm}^3 \)

---

Figure 7: Sphere

- Given: \( r = 12 \, \text{cm} \)
- Formula: \( V = \frac{4}{3} \pi r^3 \)
- Calculation:
\[
V = \frac{4}{3} \pi (12)^3 = \frac{4}{3} \pi (1728) = 2304 \pi \, \text{cm}^3
\]
- Volume: \( 2304 \pi \, \text{cm}^3 \)

---

Figure 8: Cylinder

- Given: \( r = 8 \, \text{ft} \), \( h = 6 \, \text{ft} \)
- Formula: \( V = \pi r^2 h \)
- Calculation:
\[
V = \pi (8)^2 (6) = \pi (64) (6) = 384 \pi \, \text{ft}^3
\]
- Volume: \( 384 \pi \, \text{ft}^3 \)

---

Figure 9: Cone

- Given: \( r = 3 \, \text{cm} \), \( h = 6 \, \text{cm} \)
- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Calculation:
\[
V = \frac{1}{3} \pi (3)^2 (6) = \frac{1}{3} \pi (9) (6) = \frac{1}{3} \pi (54) = 18 \pi \, \text{cm}^3
\]
- Volume: \( 18 \pi \, \text{cm}^3 \)

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Figure 10: Cone

- Given: \( d = 30 \, \text{m} \), \( h = 29 \, \text{m} \)
- Radius: \( r = \frac{d}{2} = \frac{30}{2} = 15 \, \text{m} \)
- Formula: \( V = \frac{1}{3} \pi r^2 h \)
- Calculation:
\[
V = \frac{1}{3} \pi (15)^2 (29) = \frac{1}{3} \pi (225) (29) = \frac{1}{3} \pi (6525) = 2175 \pi \, \text{m}^3
\]
- Volume: \( 2175 \pi \, \text{m}^3 \)

---

Figure 11: Cylinder

- Given: \( d = 20 \, \text{cm} \), \( h = 10 \, \text{cm} \)
- Radius: \( r = \frac{d}{2} = \frac{20}{2} = 10 \, \text{cm} \)
- Formula: \( V = \pi r^2 h \)
- Calculation:
\[
V = \pi (10)^2 (10) = \pi (100) (10) = 1000 \pi \, \text{cm}^3
\]
- Volume: \( 1000 \pi \, \text{cm}^3 \)

---

Figure 12: Sphere

- Given: \( d = 20 \, \text{cm} \)
- Radius: \( r = \frac{d}{2} = \frac{20}{2} = 10 \, \text{cm} \)
- Formula: \( V = \frac{4}{3} \pi r^3 \)
- Calculation:
\[
V = \frac{4}{3} \pi (10)^3 = \frac{4}{3} \pi (1000) = \frac{4000}{3} \pi \, \text{cm}^3
\]
- Volume: \( \frac{4000}{3} \pi \, \text{cm}^3 \)

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Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 5145 \pi \, \text{ft}^3 \\
2. & 288 \pi \, \text{in}^3 \\
3. & 240 \pi \, \text{cm}^3 \\
4. & 486 \pi \, \text{m}^3 \\
5. & 9600 \pi \, \text{in}^3 \\
6. & 36 \pi \, \text{mm}^3 \\
7. & 2304 \pi \, \text{cm}^3 \\
8. & 384 \pi \, \text{ft}^3 \\
9. & 18 \pi \, \text{cm}^3 \\
10. & 2175 \pi \, \text{m}^3 \\
11. & 1000 \pi \, \text{cm}^3 \\
12. & \frac{4000}{3} \pi \, \text{cm}^3 \\
\end{array}
}
\]