Answer:
Option D is correct.
Diameter of mega cone is, 6.5 in
Step-by-step explanation:
Volume of cone formula is given by:
.....[1] where
V represents the Volume of a cone
D represents the diameter of the cone
h represents the height of a cone.
Use : ![\pi = \frac{22}{7}](https://tex.z-dn.net/?f=%5Cpi%20%3D%20%5Cfrac%7B22%7D%7B7%7D)
As per the given statement:
A mini-cone has a diameter of 2 inches and holds 12.5
of ice cream.
⇒Diameter of mini cone(D)= 2 inches
And volume of mini cone(V)= 12.5 cubic inches.
Substitute these given values in [1] to solve for height of the mini cone(h);
![12.5 = \frac{1}{12} \times \frac{22}{7} \times(2)^2 \times h](https://tex.z-dn.net/?f=12.5%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%282%29%5E2%20%5Ctimes%20h)
or
![h = \frac{12.5 \times 12 \times 7}{22 \times 4}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B12.5%20%5Ctimes%2012%20%5Ctimes%207%7D%7B22%20%5Ctimes%204%7D)
Simplify:
in.
Since, the height of the mini cone and the height of the mega cone are same;
then;
Height of the mega cone(h) = 11.93 inches.
Also, it is given that a mega-cone holds 133.1
of ice cream
⇒ Volume of mega cone(V) = ![133.1 in^3](https://tex.z-dn.net/?f=133.1%20in%5E3)
Substitute these values in [1] to solve for D:
![133.1 = \frac{1}{12} \times \frac{22}{7} \times D^2 \times 11.93](https://tex.z-dn.net/?f=133.1%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20D%5E2%20%5Ctimes%2011.93)
or
![D^2 = \frac{133.1 \times 12 \times 7}{22 \times 11.93}](https://tex.z-dn.net/?f=D%5E2%20%3D%20%5Cfrac%7B133.1%20%5Ctimes%2012%20%5Ctimes%207%7D%7B22%20%5Ctimes%2011.93%7D)
Simplify:
![D^2 = 42.5984912](https://tex.z-dn.net/?f=D%5E2%20%3D%2042.5984912)
Taking square root both sides we get;
inces.
Therefore, the diameter of the mega cone is, 6.5 in