Question

A mini-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.

Answer 1

Option D is correct.

Diameter of mega cone is, 6.5 in

Explanation:

Volume of cone formula is given by:

`V = (1)/(12) \pi D^2h` .....[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 = (22)/(7)`

As per the given statement:

A mini-cone has a diameter of 2 inches and holds 12.5
`in^3` 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 = (1)/(12) * (22)/(7) *(2)^2 * h`

or

`h = (12.5 * 12 * 7)/(22 * 4)`

Simplify:

`h \approx 11.93` 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
`in^3` of ice cream

⇒ Volume of mega cone(V) =
`133.1 in^3`

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

`133.1 = (1)/(12) * (22)/(7) * D^2 * 11.93`

or

`D^2 = (133.1 * 12 * 7)/(22 * 11.93)`

Simplify:

`D^2 = 42.5984912`

Taking square root both sides we get;

`D = √( 42.5984912) = 6.5` inces.

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