Answer:
Option D is correct.
Diameter of mega cone is, 6.5 in
Step-by-step explanation:
Volume of cone formula is given by:
[tex]V = \frac{1}{12} \pi D^2h[/tex] .....[1] where
V represents the Volume of a cone
D represents the diameter of the cone
h represents the height of a cone.
Use : [tex]\pi = \frac{22}{7}[/tex]
As per the given statement:
A mini-cone has a diameter of 2 inches and holds 12.5 [tex]in^3[/tex] 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);
[tex]12.5 = \frac{1}{12} \times \frac{22}{7} \times(2)^2 \times h[/tex]
or
[tex]h = \frac{12.5 \times 12 \times 7}{22 \times 4}[/tex]
Simplify:
[tex]h \approx 11.93[/tex] 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 [tex]in^3[/tex] of ice cream
⇒ Volume of mega cone(V) = [tex]133.1 in^3[/tex]
Substitute these values in [1] to solve for D:
[tex]133.1 = \frac{1}{12} \times \frac{22}{7} \times D^2 \times 11.93[/tex]
or
[tex]D^2 = \frac{133.1 \times 12 \times 7}{22 \times 11.93}[/tex]
Simplify:
[tex]D^2 = 42.5984912[/tex]
Taking square root both sides we get;
[tex]D = \sqrt{ 42.5984912} = 6.5[/tex] inces.
Therefore, the diameter of the mega cone is, 6.5 in
