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Answer :
To find the height [tex]\( h \)[/tex] of the cone, we need to use the formula for the volume of a cone. The formula for the volume [tex]\( V \)[/tex] of a cone is given by:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
In this problem, the given volume of the cone is [tex]\( 147 \pi \)[/tex] cubic centimeters, and the radius [tex]\( r \)[/tex] is 7 cm. We'll plug these values into the volume formula and solve for [tex]\( h \)[/tex].
1. Substitute the known values into the volume formula:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7)^2 h \][/tex]
2. Simplify the expression by calculating [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
Now the equation becomes:
[tex]\[ 147 \pi = \frac{1}{3} \pi \times 49 \times h \][/tex]
3. To solve for [tex]\( h \)[/tex], first eliminate [tex]\( \pi \)[/tex] from both sides of the equation:
[tex]\[ 147 = \frac{1}{3} \times 49 \times h \][/tex]
4. Multiply both sides by 3 to get rid of the fraction:
[tex]\[ 147 \times 3 = 49 \times h \][/tex]
5. Calculate [tex]\( 147 \times 3 \)[/tex]:
[tex]\[ 147 \times 3 = 441 \][/tex]
So, the equation is now:
[tex]\[ 441 = 49 \times h \][/tex]
6. Finally, solve for [tex]\( h \)[/tex] by dividing both sides by 49:
[tex]\[ h = \frac{441}{49} \][/tex]
7. Calculate [tex]\( \frac{441}{49} \)[/tex] to find the height [tex]\( h \)[/tex]:
[tex]\[ h = 9 \][/tex]
So, the height of the cone is 9 cm. Therefore, the expression that can be used to find [tex]\( h \)[/tex] is:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7^2) h \][/tex]
And using this expression, the height [tex]\( h \)[/tex] is 9 cm.
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
In this problem, the given volume of the cone is [tex]\( 147 \pi \)[/tex] cubic centimeters, and the radius [tex]\( r \)[/tex] is 7 cm. We'll plug these values into the volume formula and solve for [tex]\( h \)[/tex].
1. Substitute the known values into the volume formula:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7)^2 h \][/tex]
2. Simplify the expression by calculating [tex]\( 7^2 \)[/tex]:
[tex]\[ 7^2 = 49 \][/tex]
Now the equation becomes:
[tex]\[ 147 \pi = \frac{1}{3} \pi \times 49 \times h \][/tex]
3. To solve for [tex]\( h \)[/tex], first eliminate [tex]\( \pi \)[/tex] from both sides of the equation:
[tex]\[ 147 = \frac{1}{3} \times 49 \times h \][/tex]
4. Multiply both sides by 3 to get rid of the fraction:
[tex]\[ 147 \times 3 = 49 \times h \][/tex]
5. Calculate [tex]\( 147 \times 3 \)[/tex]:
[tex]\[ 147 \times 3 = 441 \][/tex]
So, the equation is now:
[tex]\[ 441 = 49 \times h \][/tex]
6. Finally, solve for [tex]\( h \)[/tex] by dividing both sides by 49:
[tex]\[ h = \frac{441}{49} \][/tex]
7. Calculate [tex]\( \frac{441}{49} \)[/tex] to find the height [tex]\( h \)[/tex]:
[tex]\[ h = 9 \][/tex]
So, the height of the cone is 9 cm. Therefore, the expression that can be used to find [tex]\( h \)[/tex] is:
[tex]\[ 147 \pi = \frac{1}{3} \pi (7^2) h \][/tex]
And using this expression, the height [tex]\( h \)[/tex] is 9 cm.
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