To solve the problem of finding the volume of each cone, we will use the formula for the volume of a cone:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.
We will calculate the volume for each cone step by step.
---
Cone 1:
- Radius (\( r \)) = 3 cm
- Height (\( h \)) = 8 cm
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (8)
\]
\[
V = \frac{1}{3} \pi (9) (8) = \frac{1}{3} \pi (72) = 24 \pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 24 \times 3.14 = 75.36 \, \text{cm}^3
\]
Rounding to 1 decimal place:
\[
V \approx 75.4 \, \text{cm}^3
\]
---
Cone 2:
- Radius (\( r \)) = 1.5 ft (since \( 1 \frac{1}{2} \) ft = 1.5 ft)
- Height (\( h \)) = 3 ft
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (1.5)^2 (3)
\]
\[
V = \frac{1}{3} \pi (2.25) (3) = \frac{1}{3} \pi (6.75) = 2.25 \pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 2.25 \times 3.14 = 7.065 \, \text{ft}^3
\]
Rounding to 1 decimal place:
\[
V \approx 7.1 \, \text{ft}^3
\]
---
Cone 3:
- Radius (\( r \)) = 3 m (since the diameter is 6 m, so \( r = \frac{6}{2} = 3 \) m)
- Height (\( h \)) = 4.2 m
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (3)^2 (4.2)
\]
\[
V = \frac{1}{3} \pi (9) (4.2) = \frac{1}{3} \pi (37.8) = 12.6 \pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 12.6 \times 3.14 = 39.564 \, \text{m}^3
\]
Rounding to 1 decimal place:
\[
V \approx 39.6 \, \text{m}^3
\]
---
Cone 4:
- Radius (\( r \)) = 4.5 in (since \( 4 \frac{1}{2} \) in = 4.5 in)
- Height (\( h \)) = 8.5 in (since \( 8 \frac{1}{2} \) in = 8.5 in)
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (4.5)^2 (8.5)
\]
\[
V = \frac{1}{3} \pi (20.25) (8.5) = \frac{1}{3} \pi (172.125) = 57.375 \pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 57.375 \times 3.14 = 179.985 \, \text{in}^3
\]
Rounding to 1 decimal place:
\[
V \approx 180.0 \, \text{in}^3
\]
---
Cone 5:
- Radius (\( r \)) = 9 cm (since the diameter is 18 cm, so \( r = \frac{18}{2} = 9 \) cm)
- Height (\( h \)) = 5 cm
\[
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (9)^2 (5)
\]
\[
V = \frac{1}{3} \pi (81) (5) = \frac{1}{3} \pi (405) = 135 \pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 135 \times 3.14 = 423.9 \, \text{cm}^3
\]
Rounding to 1 decimal place:
\[
V \approx 423.9 \, \text{cm}^3
\]
---
Final Answers:
\[
\boxed{
\begin{array}{c|c}
\text{Cone} & \text{Volume} \\
\hline
1 & 75.4 \, \text{cm}^3 \\
2 & 7.1 \, \text{ft}^3 \\
3 & 39.6 \, \text{m}^3 \\
4 & 180.0 \, \text{in}^3 \\
5 & 423.9 \, \text{cm}^3 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of cone volume worksheet.
