College

The radius of a cone is 2.5 units. The volume of the cone is 19 cubic units. Complete the cone by dragging each number to the correct location on the fraction. Not all numbers will be used.

Available numbers:
- 57
- 19
- 7.5
- 6.25
- 2.5

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.