Amini-cone has a diameter of 2 inches and holds 12.5 in3 of ice cream. a mega-cone holds 133.1 in3 of ice cream. if the cones have the same height, what is the diameter of the mega-cone? a. 3.25 in. b. 4.4 in. c. 6 in. d. 6.5 in.

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 :

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);

or

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) =

Substitute these values in [1] to solve for D:

or

Simplify:

Taking square root both sides we get;

inces.

Therefore, the diameter of the mega cone is, 6.5 in

any options?

step-by-step explanation: