College

The radius of a cone is 2.5 units. The volume of the cone is 19 cubic units. Complete the expression that represents the height of the cone.

Drag each number to the correct location on the fraction. Not all numbers will be used.

Choices:
- 6.25
- 7.5
- 19
- 2.5
- 57

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.