Subjects geometry

Cylinder Circle Bb8B14

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1. **State the problem:** Find the volume of a cylinder and the area of a circle with radius $r=21$ cm. 2. **Formulas:** - Volume of a cylinder: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. - Area of a circle: $$A = \pi r^2$$ 3. **Important note:** The problem does not provide the height $h$ of the cylinder, so we can only find the volume formula in terms of $h$ or assume a height if given. 4. **Calculate the area of the circle:** $$A = \pi (21)^2 = \pi \times 441 = 441\pi \text{ cm}^2$$ 5. **Express the volume of the cylinder:** $$V = \pi (21)^2 h = 441\pi h \text{ cm}^3$$ Since $h$ is unknown, the volume is $441\pi h$ cubic centimeters. **Final answers:** - Area of the circle: $441\pi$ cm$^2$ - Volume of the cylinder: $441\pi h$ cm$^3$ (depends on height $h$)