To determine which figures have a volume greater than 600 cubic inches, we'll calculate the volume of each figure using the given dimensions and the formula for the volume of each shape.
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Volume of the Cylinder: The formula for the volume \( V \) of a cylinder is: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. Given \( r = 6 \) and \( h = 15 \): \[ V = 3.14 \times (6^2) \times 15 \] \[ V = 3.14 \times 36 \times 15 \] \[ V = 3.14 \times 540 \] \[ V = 1695.6 \text{ cubic inches} \]
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Volume of the Cone: The formula for the volume \( V \) of a cone is: \[ V = \frac{1}{3} \pi r^2 h \] Given \( r = 6 \) and \( h = 15 \): \[ V = \frac{1}{3} \times 3.14 \times (6^2) \times 15 \] \[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \] \[ V = \frac{1}{3} \times 3.14 \times 540 \] \[ V = \frac{1}{3} \times 1696.2 \] \[ V = 565.2 \text{ cubic inches} \]
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Volume of the Sphere: The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] Given \( r = 6 \): \[ V = \frac{4}{3} \times 3.14 \times (6^3) \] \[ V = \frac{4}{3} \times 3.14 \times 216 \] \[ V = \frac{4}{3} \times 678.24 \] \[ V = 902.99 \text{ cubic inches} \]
Summary of Volumes:
- Cylinder: \( 1695.6 \) cubic inches
- Cone: \( 565.2 \) cubic inches
- Sphere: \( 904.32 \) cubic inches
Conclusion:
Figures with a volume greater than 600 cubic inches are:
- Cylinder (1695.6 cubic inches)
- Sphere (904.32 cubic inches)
The Cone does not exceed 600 cubic inches with its volume of \( 565.2 \) cubic inches.
Final Answer: Cylinder, Sphere
3 answers