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.

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**Problem 1:**

The volume $$ V $$ of a cone is given by  
$$
V = \frac{1}{3} \pi r^2 h
$$
For a cone with radius $$ r = 5 $$ feet and height $$ h = 7 $$ feet, we have:
$$
V = \frac{1}{3} \pi (5^2)(7) = \frac{1}{3} \pi (25)(7) = \frac{175}{3} \pi \text{ cubic feet}
$$

Using $$ \pi = 3.14 $$:
$$
V \approx \frac{175}{3} \times 3.14 \approx \frac{549.5}{3} \approx 183.17 \text{ cubic feet}
$$

Since the oil is released at a rate of 20 cubic feet per minute, the time $$ t $$ needed to empty the container is:
$$
t = \frac{V}{\text{rate}} = \frac{183.17}{20} \approx 9.16 \text{ minutes}
$$

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**Problem 2:**

Given a cone with radius $$ r = 7 $$ cm and height $$ h = 12 $$ cm, the volume is:
$$
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (7^2)(12) = \frac{1}{3} \pi (49)(12)
$$
$$
V = \frac{1}{3} \pi (588) = 196 \pi \text{ cubic centimeters}
$$

Thus, the volume of the cone is $$ 196 \pi $$ cubic centimeters. If you wish to use $$ \pi = 3.14 $$, then:
$$
V \approx 196 \times 3.14 \approx 615.44 \text{ cubic centimeters}
$$
**Problem 1:** - Volume of the cone: Approximately 183.17 cubic feet. - Time to empty: About 9.16 minutes. **Problem 2:** - Volume of the cone: $$ 196\pi $$ cubic centimeters or approximately 615.44 cubic centimeters.

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