Question

Which conical container holds more water? Cone 1: height: 8 Diamiter: 4 Cone 2: Height 8 Diamiter 6 Figure not drawn to scale.

Answer 1

To compare the volumes of the two cones, we can use the formula for the volume of a cone:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

### Cone 1
- Height (\( h_1 \)): 8
- Diameter: 4 → Radius (\( r_1 \)): \( \frac{4}{2} = 2 \)

Calculating the volume of Cone 1:

\[
V_1 = \frac{1}{3} \pi (2)^2 (8)
\]
\[
V_1 = \frac{1}{3} \pi (4)(8)
\]
\[
V_1 = \frac{32}{3} \pi
\]

### Cone 2
- Height (\( h_2 \)): 8
- Diameter: 6 → Radius (\( r_2 \)): \( \frac{6}{2} = 3 \)

Calculating the volume of Cone 2:

\[
V_2 = \frac{1}{3} \pi (3)^2 (8)
\]
\[
V_2 = \frac{1}{3} \pi (9)(8)
\]
\[
V_2 = \frac{72}{3} \pi
\]
\[
V_2 = 24 \pi
\]

### Comparing Volumes
Now, we have:

- Volume of Cone 1: \( \frac{32}{3} \pi \)
- Volume of Cone 2: \( 24 \pi \)

To make the comparison easier, we can express \( 24 \pi \) with the same denominator as \( \frac{32}{3} \pi \):

\[
24 \pi = \frac{72}{3} \pi
\]

Now it is easier to compare:

- Cone 1: \( \frac{32}{3} \pi \)
- Cone 2: \( \frac{72}{3} \pi \)

Clearly, since \( \frac{72}{3} > \frac{32}{3} \), Cone 2 holds more water.

### Conclusion
**Cone 2 holds more water.**