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Answer :
To find the height of a cone when the radius and the volume are given, we use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( h \)[/tex] is the height of the cone,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
In this problem:
- The volume [tex]\( V \)[/tex] is 19 cubic units.
- The radius [tex]\( r \)[/tex] is 2.5 units.
We need to find the height [tex]\( h \)[/tex]. First, let's rearrange the volume formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Next, substitute the known values into the formula:
1. Calculate the value of [tex]\( \pi \times r^2 \)[/tex]:
- [tex]\( r^2 = 2.5^2 = 6.25 \)[/tex]
- So, [tex]\( \pi \times r^2 \approx 3.14159 \times 6.25 \approx 19.6349375 \)[/tex]
2. Now plug the values into the formula for height:
[tex]\[ h = \frac{3 \times 19}{19.6349375} \][/tex]
3. Perform the calculation:
[tex]\[ h \approx \frac{57}{19.6349375} \][/tex]
After performing these calculations, the height [tex]\( h \)[/tex] of the cone is found to be approximately 2.903 units.
Therefore, the height of the cone is approximately 2.903 units.
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( h \)[/tex] is the height of the cone,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
In this problem:
- The volume [tex]\( V \)[/tex] is 19 cubic units.
- The radius [tex]\( r \)[/tex] is 2.5 units.
We need to find the height [tex]\( h \)[/tex]. First, let's rearrange the volume formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Next, substitute the known values into the formula:
1. Calculate the value of [tex]\( \pi \times r^2 \)[/tex]:
- [tex]\( r^2 = 2.5^2 = 6.25 \)[/tex]
- So, [tex]\( \pi \times r^2 \approx 3.14159 \times 6.25 \approx 19.6349375 \)[/tex]
2. Now plug the values into the formula for height:
[tex]\[ h = \frac{3 \times 19}{19.6349375} \][/tex]
3. Perform the calculation:
[tex]\[ h \approx \frac{57}{19.6349375} \][/tex]
After performing these calculations, the height [tex]\( h \)[/tex] of the cone is found to be approximately 2.903 units.
Therefore, the height of the cone is approximately 2.903 units.
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