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Answer :
To find the height [tex]\( h \)[/tex] of a cone, we can use the formula for the volume of a cone. The volume [tex]\( V \)[/tex] of a cone is given by:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height of the cone.
In the problem, we are provided with the following information:
- The volume of the cone is [tex]\( 147 \pi \)[/tex] cubic centimeters.
- The radius [tex]\( r \)[/tex] of the base is 7 cm.
Substituting these values into the volume formula, we get:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7^2) h \][/tex]
Now, let's simplify and understand this equation step-by-step:
1. The radius part in the formula becomes [tex]\( 7^2 = 49 \)[/tex].
2. Substitute [tex]\( 49 \)[/tex] into the equation:
[tex]\[ 147 \pi = \frac{1}{3} \pi (49) h \][/tex]
3. We see that this matches with one of the answer choices:
- [tex]\( \boxed{147 \pi = \frac{1}{3} \pi (7^2) h} \)[/tex]
This expression correctly matches the equation needed to solve for the height [tex]\( h \)[/tex] of the cone.
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height of the cone.
In the problem, we are provided with the following information:
- The volume of the cone is [tex]\( 147 \pi \)[/tex] cubic centimeters.
- The radius [tex]\( r \)[/tex] of the base is 7 cm.
Substituting these values into the volume formula, we get:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7^2) h \][/tex]
Now, let's simplify and understand this equation step-by-step:
1. The radius part in the formula becomes [tex]\( 7^2 = 49 \)[/tex].
2. Substitute [tex]\( 49 \)[/tex] into the equation:
[tex]\[ 147 \pi = \frac{1}{3} \pi (49) h \][/tex]
3. We see that this matches with one of the answer choices:
- [tex]\( \boxed{147 \pi = \frac{1}{3} \pi (7^2) h} \)[/tex]
This expression correctly matches the equation needed to solve for the height [tex]\( h \)[/tex] of the cone.
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