Answer :
* The volume of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$.
* Substitute the given values $V = 147\pi$ and $r = 7$ into the formula: $147\pi = \frac{1}{3} \pi (7^2) h$.
* Simplify the equation: $147\pi = \frac{1}{3} \pi (49) h$.
* The correct expression to find $h$ is: $\boxed{147 \pi=\frac{1}{3} \pi(7^2)(h)}$.
### Explanation
1. State the formula and given values
We are given the volume of a cone, $V = 147
\pi$ cubic centimeters, and the radius, $r = 7$ cm. We want to find the expression that can be used to find the height, $h$, of the cone. The formula for the volume of a cone is given by:
$$V = \frac{1}{3} \pi r^2 h$$
We will substitute the given values into this formula.
2. Substitute the values
Substitute $V = 147\pi$ and $r = 7$ into the formula:
$$147\pi = \frac{1}{3} \pi (7^2) h$$
$$147\pi = \frac{1}{3} \pi (49) h$$
3. Compare with the options
Now we compare this equation with the given options:
Option 1: $147 x=\frac{1}{3}(7)(h)^2$
Option 2: $147 \pi=\frac{1}{3} \pi(7^2)(h)$
Option 3: $147 k=\frac{1}{3} \pi h$
Option 4: $147 \pi=\frac{1}{3} \pi(7)(h)$
Comparing the equation $147\pi = \frac{1}{3} \pi (49) h$ with the options, we see that Option 2 matches exactly.
4. Final Answer
Therefore, the expression that can be used to find $h$ is:
$$147 \pi = \frac{1}{3} \pi (7^2) h$$
So the correct answer is option 2.
### Examples
Cones are not just theoretical shapes; they appear everywhere in the real world! Think of ice cream cones, traffic cones, or even the conical roofs of some buildings. Understanding how to calculate the volume and dimensions of a cone is super useful in many practical situations, from figuring out how much ice cream fits in a cone to designing structures.
* Substitute the given values $V = 147\pi$ and $r = 7$ into the formula: $147\pi = \frac{1}{3} \pi (7^2) h$.
* Simplify the equation: $147\pi = \frac{1}{3} \pi (49) h$.
* The correct expression to find $h$ is: $\boxed{147 \pi=\frac{1}{3} \pi(7^2)(h)}$.
### Explanation
1. State the formula and given values
We are given the volume of a cone, $V = 147
\pi$ cubic centimeters, and the radius, $r = 7$ cm. We want to find the expression that can be used to find the height, $h$, of the cone. The formula for the volume of a cone is given by:
$$V = \frac{1}{3} \pi r^2 h$$
We will substitute the given values into this formula.
2. Substitute the values
Substitute $V = 147\pi$ and $r = 7$ into the formula:
$$147\pi = \frac{1}{3} \pi (7^2) h$$
$$147\pi = \frac{1}{3} \pi (49) h$$
3. Compare with the options
Now we compare this equation with the given options:
Option 1: $147 x=\frac{1}{3}(7)(h)^2$
Option 2: $147 \pi=\frac{1}{3} \pi(7^2)(h)$
Option 3: $147 k=\frac{1}{3} \pi h$
Option 4: $147 \pi=\frac{1}{3} \pi(7)(h)$
Comparing the equation $147\pi = \frac{1}{3} \pi (49) h$ with the options, we see that Option 2 matches exactly.
4. Final Answer
Therefore, the expression that can be used to find $h$ is:
$$147 \pi = \frac{1}{3} \pi (7^2) h$$
So the correct answer is option 2.
### Examples
Cones are not just theoretical shapes; they appear everywhere in the real world! Think of ice cream cones, traffic cones, or even the conical roofs of some buildings. Understanding how to calculate the volume and dimensions of a cone is super useful in many practical situations, from figuring out how much ice cream fits in a cone to designing structures.
