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Answer :
To find the height of the cone, let's use the formula for the volume of a cone:
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( \text{Volume} \)[/tex] is 19 cubic units,
- [tex]\( r \)[/tex] (radius) is 2.5 units,
- [tex]\( h \)[/tex] is the height we need to find,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
We need to solve this equation for the height [tex]\( h \)[/tex]. Let's rearrange the formula:
[tex]\[ h = \frac{3 \times \text{Volume}}{\pi \times r^2} \][/tex]
Let's substitute the values we know:
1. Plug in the volume (19 cubic units) and the radius (2.5 units) into the formula.
2. Calculate the denominator: [tex]\(\pi \times (2.5)^2\)[/tex].
3. Divide the product of the volume multiplied by 3 by this result to find [tex]\( h \)[/tex].
When we perform this calculation, we'll find that the height [tex]\( h \)[/tex] of the cone is approximately 2.90 units.
This value completes the details of the cone given the radius and volume provided.
[tex]\[ \text{Volume} = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( \text{Volume} \)[/tex] is 19 cubic units,
- [tex]\( r \)[/tex] (radius) is 2.5 units,
- [tex]\( h \)[/tex] is the height we need to find,
- [tex]\( \pi \)[/tex] is approximately 3.14159.
We need to solve this equation for the height [tex]\( h \)[/tex]. Let's rearrange the formula:
[tex]\[ h = \frac{3 \times \text{Volume}}{\pi \times r^2} \][/tex]
Let's substitute the values we know:
1. Plug in the volume (19 cubic units) and the radius (2.5 units) into the formula.
2. Calculate the denominator: [tex]\(\pi \times (2.5)^2\)[/tex].
3. Divide the product of the volume multiplied by 3 by this result to find [tex]\( h \)[/tex].
When we perform this calculation, we'll find that the height [tex]\( h \)[/tex] of the cone is approximately 2.90 units.
This value completes the details of the cone given the radius and volume provided.
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