Volume of Pyramids & Cones Worksheets by Teacher Mine | TPT - Free Printable

The worksheet provided involves calculating the volume of pyramids and cones. The formulas for these calculations are as follows:

Volume Formulas:

1. Volume of a Pyramid:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

2. Volume of a Cone:
\[
V = \frac{1}{3} \times \pi \times r^2 \times h
\]
where \( r \) is the radius of the base, and \( h \) is the height.

Steps to Solve Each Problem:

For each problem, we need to:
1. Identify whether the shape is a pyramid or a cone.
2. Determine the given dimensions (e.g., base area, height, radius).
3. Use the appropriate formula to calculate the volume.
4. Round the answer to the nearest tenth if necessary.

---

Detailed Solutions:

#### Problem 1:
- Shape: Pyramid
- Base Area: \( 8 \)
- Height: \( 6 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 8 \times 6 = \frac{1}{3} \times 48 = 16
\]
- Answer: \( 16 \)

#### Problem 2:
- Shape: Cone
- Radius (\( r \)): \( 5 \)
- Height (\( h \)): \( 12 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 5^2 \times 12 = \frac{1}{3} \times \pi \times 25 \times 12 = \frac{1}{3} \times 300\pi = 100\pi
\]
- Approximation: \( 100\pi \approx 314.16 \)
- Answer: \( 314.2 \)

#### Problem 3:
- Shape: Pyramid
- Base Area: \( 13 \)
- Height: \( 7 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 13 \times 7 = \frac{1}{3} \times 91 = 30.33
\]
- Answer: \( 30.3 \)

#### Problem 4:
- Shape: Cone
- Radius (\( r \)): \( 7 \)
- Height (\( h \)): \( 15 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 7^2 \times 15 = \frac{1}{3} \times \pi \times 49 \times 15 = \frac{1}{3} \times 735\pi = 245\pi
\]
- Approximation: \( 245\pi \approx 770.85 \)
- Answer: \( 770.9 \)

#### Problem 5:
- Shape: Pyramid
- Base Area: \( 8 \)
- Height: \( 9 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 8 \times 9 = \frac{1}{3} \times 72 = 24
\]
- Answer: \( 24 \)

#### Problem 6:
- Shape: Cone
- Radius (\( r \)): \( 2 \)
- Height (\( h \)): \( 12 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 2^2 \times 12 = \frac{1}{3} \times \pi \times 4 \times 12 = \frac{1}{3} \times 48\pi = 16\pi
\]
- Approximation: \( 16\pi \approx 50.27 \)
- Answer: \( 50.3 \)

#### Problem 7:
- Shape: Pyramid
- Base Area: \( 7 \)
- Height: \( 10 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 7 \times 10 = \frac{1}{3} \times 70 = 23.33
\]
- Answer: \( 23.3 \)

#### Problem 8:
- Shape: Cone
- Radius (\( r \)): \( 7 \)
- Height (\( h \)): \( 12 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 7^2 \times 12 = \frac{1}{3} \times \pi \times 49 \times 12 = \frac{1}{3} \times 588\pi = 196\pi
\]
- Approximation: \( 196\pi \approx 615.75 \)
- Answer: \( 615.8 \)

#### Problem 9:
- Shape: Pyramid
- Base Area: \( 9 \)
- Height: \( 12 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 9 \times 12 = \frac{1}{3} \times 108 = 36
\]
- Answer: \( 36 \)

#### Problem 10:
- Shape: Cone
- Radius (\( r \)): \( 9 \)
- Height (\( h \)): \( 15 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 9^2 \times 15 = \frac{1}{3} \times \pi \times 81 \times 15 = \frac{1}{3} \times 1215\pi = 405\pi
\]
- Approximation: \( 405\pi \approx 1272.35 \)
- Answer: \( 1272.4 \)

#### Problem 11:
- Shape: Pyramid
- Base Area: \( 12 \)
- Height: \( 15 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 12 \times 15 = \frac{1}{3} \times 180 = 60
\]
- Answer: \( 60 \)

#### Problem 12:
- Shape: Cone
- Radius (\( r \)): \( 5 \)
- Height (\( h \)): \( 12 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 5^2 \times 12 = \frac{1}{3} \times \pi \times 25 \times 12 = \frac{1}{3} \times 300\pi = 100\pi
\]
- Approximation: \( 100\pi \approx 314.16 \)
- Answer: \( 314.2 \)

#### Problem 13:
- Shape: Pyramid
- Base Area: \( 15 \)
- Height: \( 18 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 15 \times 18 = \frac{1}{3} \times 270 = 90
\]
- Answer: \( 90 \)

#### Problem 14:
- Shape: Cone
- Radius (\( r \)): \( 6 \)
- Height (\( h \)): \( 15 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 6^2 \times 15 = \frac{1}{3} \times \pi \times 36 \times 15 = \frac{1}{3} \times 540\pi = 180\pi
\]
- Approximation: \( 180\pi \approx 565.49 \)
- Answer: \( 565.5 \)

#### Problem 15:
- Shape: Pyramid
- Base Area: \( 1300 \)
- Height: \( 15 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 1300 \times 15 = \frac{1}{3} \times 19500 = 6500
\]
- Answer: \( 6500 \)

#### Problem 16:
- Shape: Cone
- Radius (\( r \)): \( 3 \)
- Height (\( h \)): \( 12 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 3^2 \times 12 = \frac{1}{3} \times \pi \times 9 \times 12 = \frac{1}{3} \times 108\pi = 36\pi
\]
- Approximation: \( 36\pi \approx 113.10 \)
- Answer: \( 113.1 \)

#### Problem 17:
- Shape: Pyramid
- Base Area: \( 296 \)
- Height: \( 12 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 296 \times 12 = \frac{1}{3} \times 3552 = 1184
\]
- Answer: \( 1184 \)

#### Problem 18:
- Shape: Cone
- Radius (\( r \)): \( 7 \)
- Height (\( h \)): \( 15 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 7^2 \times 15 = \frac{1}{3} \times \pi \times 49 \times 15 = \frac{1}{3} \times 735\pi = 245\pi
\]
- Approximation: \( 245\pi \approx 770.85 \)
- Answer: \( 770.9 \)

#### Problem 19:
- Shape: Pyramid
- Base Area: \( 60 \)
- Height: \( 12 \)
- Formula: \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)
- Calculation:
\[
V = \frac{1}{3} \times 60 \times 12 = \frac{1}{3} \times 720 = 240
\]
- Answer: \( 240 \)

#### Problem 20:
- Shape: Cone
- Radius (\( r \)): \( 7 \)
- Height (\( h \)): \( 15 \)
- Formula: \( V = \frac{1}{3} \times \pi \times r^2 \times h \)
- Calculation:
\[
V = \frac{1}{3} \times \pi \times 7^2 \times 15 = \frac{1}{3} \times \pi \times 49 \times 15 = \frac{1}{3} \times 735\pi = 245\pi
\]
- Approximation: \( 245\pi \approx 770.85 \)
- Answer: \( 770.9 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 16 \\
2. & 314.2 \\
3. & 30.3 \\
4. & 770.9 \\
5. & 24 \\
6. & 50.3 \\
7. & 23.3 \\
8. & 615.8 \\
9. & 36 \\
10. & 1272.4 \\
11. & 60 \\
12. & 314.2 \\
13. & 90 \\
14. & 565.5 \\
15. & 6500 \\
16. & 113.1 \\
17. & 1184 \\
18. & 770.9 \\
19. & 240 \\
20. & 770.9 \\
\end{array}
}
\]