Name: cayyarmasin Date \( \qquad \) Solve the problems, A container is shaped like a cone and contains oil. The radius is 5 feet and the height is 7 feet. If 1) the container can release oil from its bottom at the rate of 20 cubic feet per minute, how long would it take for the container to empty fully? Use ( \( \pi=3.14 \) ), 2) Calculate the volume of a cone if the height is 12 cm and the radius is 7 cm.

To find out how long it would take to empty the cone-shaped container, we first need to calculate the volume of the cone. The formula for the volume of a cone is: \[ V = \frac{1}{3} \pi r^2 h \] For the first problem, with a radius of 5 feet and a height of 7 feet: \[ V = \frac{1}{3} \times 3.14 \times (5^2) \times 7 = \frac{1}{3} \times 3.14 \times 25 \times 7 = \frac{1}{3} \times 551.5 \approx 183.83 \text{ cubic feet} \] Now, if the container releases oil at the rate of 20 cubic feet per minute, the time to empty the container is: \[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} = \frac{183.83}{20} \approx 9.19 \text{ minutes} \] For the second problem, to calculate the volume of a cone with a height of 12 cm and a radius of 7 cm: \[ V = \frac{1}{3} \pi r^2 h \] \[ V = \frac{1}{3} \times 3.14 \times (7^2) \times 12 = \frac{1}{3} \times 3.14 \times 49 \times 12 = \frac{1}{3} \times 1847.76 \approx 615.92 \text{ cm}^3 \] So, the total time to empty the container is approximately 9.19 minutes, and the volume of the cone is approximately 615.92 cm³.