To determine which figures have a volume greater than 600 cubic inches, we need to calculate the volume for each figure and compare it to 600 cubic inches. The formulas for the volumes of the shapes are as follows:
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Cylinder: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
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Cone: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
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Sphere: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius.
Step 1: Calculate the volumes.
Since the problem does not specify dimensions (radii or heights) for the cylinders, cones, and spheres, I will use some reasonable example values for \( r \) and \( h \).
Example Values:
- Cylinder: \( r = 6 \), \( h = 10 \)
- Cone: \( r = 6 \), \( h = 10 \)
- Sphere: \( r = 8 \)
1. Volume of the Cylinder
\[ V = 3.14 \times (6^2) \times 10 \] \[ = 3.14 \times 36 \times 10 \] \[ = 3.14 \times 360 \] \[ = 1130.4 \text{ cubic inches} \]
2. Volume of the Cone
\[ V = \frac{1}{3} \times 3.14 \times (6^2) \times 10 \] \[ = \frac{1}{3} \times 3.14 \times 36 \times 10 \] \[ = \frac{1}{3} \times 3.14 \times 360 \] \[ = \frac{1130.4}{3} \] \[ = 376.8 \text{ cubic inches} \]
3. Volume of the Sphere
\[ V = \frac{4}{3} \times 3.14 \times (8^3) \] \[ = \frac{4}{3} \times 3.14 \times 512 \] \[ = \frac{4 \times 3.14 \times 512}{3} \] \[ = \frac{6428.48}{3} \] \[ \approx 2142.83 \text{ cubic inches} \]
Step 2: Compare to 600 cubic inches
- Cylinder Volume: 1130.4 cubic inches (greater than 600)
- Cone Volume: 376.8 cubic inches (not greater than 600)
- Sphere Volume: 2142.83 cubic inches (greater than 600)
Conclusion
The figures with a volume greater than 600 cubic inches are:
- Cylinder
- Sphere