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The volume of a cone is [tex]$50 \pi$[/tex] cubic feet. Its height is 6 feet. In feet, what is the radius of the cone? Round your answer to the nearest tenth.

[tex]\square[/tex]

Sagot :

GinnyAnswer
To find the radius of the cone given its volume and height, we can use the formula for the volume of a cone:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

Given:
- Volume [tex]\(V = 50 \pi\)[/tex] cubic feet
- Height [tex]\(h = 6\)[/tex] feet

We need to find the radius [tex]\(r\)[/tex]. First, solve the volume formula for [tex]\(r^2\)[/tex]:

[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]

Rearrange to solve for [tex]\(r^2\)[/tex]:

[tex]\[ r^2 = \frac{3V}{\pi h} \][/tex]

Substitute the given values into the equation:

[tex]\[ r^2 = \frac{3 \cdot 50 \pi}{\pi \cdot 6} \][/tex]

Simplify the right-hand side:

[tex]\[ r^2 = \frac{150 \pi}{6 \pi} = \frac{150}{6} = 25 \][/tex]

Thus,

[tex]\[ r^2 = 25 \][/tex]

Now, take the square root of both sides to find [tex]\(r\)[/tex]:

[tex]\[ r = \sqrt{25} = 5 \][/tex]

Finally, we round the radius to the nearest tenth, but in this case, it is an exact number:

[tex]\[ \boxed{5.0} \][/tex]

So, the radius of the cone is 5.0 feet.
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