Subjects geometry

Cone Volume Cost 0Ebd93

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1. **State the problem:** We need to find the cost to fill a conical silo with rice. The silo has a height $h=7$ meters and a base radius $r=1.5$ meters. Rice costs 204 per cubic meter. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ 3. **Substitute the given values:** $$V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 7$$ 4. **Calculate the radius squared:** $$1.5^2 = 2.25$$ 5. **Calculate the volume:** $$V = \frac{1}{3} \times 3.14 \times 2.25 \times 7$$ 6. **Multiply the constants:** $$3.14 \times 2.25 = 7.065$$ 7. **Continue volume calculation:** $$V = \frac{1}{3} \times 7.065 \times 7$$ 8. **Multiply 7.065 by 7:** $$7.065 \times 7 = 49.455$$ 9. **Divide by 3:** $$V = \frac{\cancel{49.455}}{\cancel{3}} = 16.485$$ 10. **Calculate the cost to fill the silo:** $$\text{Cost} = 16.485 \times 204 = 3364.74$$ **Final answer:** The cost to fill the silo with rice is 3364.74.