The volume of a cone is 27∏ and the radius is 3. Can you find the length of the height?

My teacher requires work if it is not too much of a hassle please SHOW WORK!!!! thank you for helping.

Answer 1

The height is #9# units

The volume of the cone is given as #27pi# (unknown) cubic units. You can make it a big cone that you can walk into and use #m^3# or a small cone sitting on your table and use #cm^3#

The volume of a cone is: #V = pir^2 (h/3)#

Then: #27pi = pi(3)^2 (h/3)#

#27pi = pi(3)h#

#9pi = pih#

#h = 9# units

If you started with the big cone, the height is #9m# or #30ft#, and if you decided on the small cone, the height is #9cm # or #3.5# inches.

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Answer 2

Sadie Adams

Using the formula for the volume of a cone, V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height, we can rearrange the formula to solve for h: h = (3V) / (πr^2). Substituting the given values, we get h = (3 * 27π) / (π * 3^2) = 27 / 3 = 9. Therefore, the height of the cone is 9 units.

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Answer 3

Wyatt Anderson

Yes, we can find the length of the height (( h )) of the cone using the formula for the volume of a cone:

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

Given that the volume ( V ) is ( 27 \pi ) and the radius ( r ) is ( 3 ), we can substitute these values into the formula and solve for ( h ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.