Subjects geometry

Toothpaste Volume 51560C

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1. **State the problem:** We need to estimate the volume of a cylinder-shaped blob of toothpaste with length (height) $h = 0.75$ cm and diameter $d = 0.5$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radius:** The radius $r$ is half the diameter, $$r = \frac{d}{2} = \frac{0.5}{2} = 0.25 \text{ cm}$$ 4. **Substitute values:** Using $\pi = 3.14$, $$V = 3.14 \times (0.25)^2 \times 0.75$$ 5. **Calculate intermediate steps:** $$0.25^2 = 0.0625$$ 6. **Calculate volume:** $$V = 3.14 \times 0.0625 \times 0.75$$ 7. **Multiply:** $$3.14 \times 0.0625 = 0.19625$$ 8. **Multiply by height:** $$0.19625 \times 0.75 = 0.1471875$$ 9. **Round to 2 decimal places:** $$V \approx 0.15 \text{ cm}^3$$ **Final answer:** The volume of toothpaste used is approximately **0.15 cm³**.
0.75 cm0.5 cm