Answer :
To determine the height of a cone with a given base radius and volume, we use the volume formula for 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, and
- [tex]\( h \)[/tex] is the height of the cone.
Given:
- The radius [tex]\( r = 4 \)[/tex] meters,
- The volume [tex]\( V = 40 \)[/tex] cubic meters.
We need to solve for the height [tex]\( h \)[/tex]. First, we rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Substitute the given values into the equation:
[tex]\[ h = \frac{3 \times 40}{\pi \times 4^2} \][/tex]
Calculate the denominator:
[tex]\[ \pi \times 4^2 = \pi \times 16 \][/tex]
Then the equation for [tex]\( h \)[/tex] becomes:
[tex]\[ h = \frac{120}{16\pi} \][/tex]
Next, calculate the value of [tex]\( h \)[/tex]:
[tex]\[ h = \frac{120}{16 \times 3.141592653589793} \][/tex]
Simplify this further:
[tex]\[ h = \frac{120}{50.26548245743669} \][/tex]
[tex]\[ h \approx 2.39 \, \text{meters} \][/tex]
To the nearest tenth, the height [tex]\( h \)[/tex] is:
[tex]\[ h \approx 2.4 \, \text{meters} \][/tex]
So, the height of the cone is approximately 2.4 meters.
[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, and
- [tex]\( h \)[/tex] is the height of the cone.
Given:
- The radius [tex]\( r = 4 \)[/tex] meters,
- The volume [tex]\( V = 40 \)[/tex] cubic meters.
We need to solve for the height [tex]\( h \)[/tex]. First, we rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Substitute the given values into the equation:
[tex]\[ h = \frac{3 \times 40}{\pi \times 4^2} \][/tex]
Calculate the denominator:
[tex]\[ \pi \times 4^2 = \pi \times 16 \][/tex]
Then the equation for [tex]\( h \)[/tex] becomes:
[tex]\[ h = \frac{120}{16\pi} \][/tex]
Next, calculate the value of [tex]\( h \)[/tex]:
[tex]\[ h = \frac{120}{16 \times 3.141592653589793} \][/tex]
Simplify this further:
[tex]\[ h = \frac{120}{50.26548245743669} \][/tex]
[tex]\[ h \approx 2.39 \, \text{meters} \][/tex]
To the nearest tenth, the height [tex]\( h \)[/tex] is:
[tex]\[ h \approx 2.4 \, \text{meters} \][/tex]
So, the height of the cone is approximately 2.4 meters.
