What is the diameter of a cone with a height of 10 yards and a volume of 92.4 cubic yards? Round to the nearest whole number.
Well what info do you have? You have the height and volume. What formula does those fit into?
V = (1/3) (pi) (r^2) (h)
AKA
Volume = 1/3 pi r squared multiplied by height
SO. Plug in your numbers,
92.4 = 1/3 (pi) (r^2) 10
Now you want diameter, so r x 2 works as well since radius is half a diameter.
Isolate the variable.
92.4 x 3 / (pi)10 = r^2
Still following? great :D
Ok now you need to divide 92.4(3) by ten and pi.
This gives you 8.8235500450146774...etc.
Leave this number in your calculator, you don't want to round quite yet.
Next,
take the square root of this number, to free 'r' from the power of two.
This gives you---> r = 2.970446102
Now you can multiply that by two, because your answer (2.970446102) is only the radius, and you need the diameter.
Your final answer would then be 5.940892204.
Now you can round :) The nearest whole number is 6, and this is your final answer :D
Hope this helped :D