A mini-cone has a diameter of 2 inches at the widest point and holds 12.5 in3 of ice cream. A mega-cone holds 133.1 in3 of ice cream. What is the diameter of the mega-cone at its widest point?
133.1/12.5 = 10.648
Assuming similarity of shape, the diameter of the larger cone is ∛10.648=2.2 times as large, or 4.4 inches.
Thanks!
To solve this problem, we'll use the concept of ratios.
First, let's calculate the ratio of the volume of the mini-cone to the volume of the mega-cone. We have:
Volume of mini-cone: 12.5 in³
Volume of mega-cone: 133.1 in³
Now, let's find the ratio:
Ratio = Volume of mini-cone / Volume of mega-cone
= 12.5 in³ / 133.1 in³
≈ 0.094
Next, let's find the relationship between the diameters of the mini-cone and the mega-cone. Since the volumes of cones are proportional to the cubes of their diameters, we can write:
Ratio = (Diameter of mini-cone / Diameter of mega-cone)³
Now, rearrange the equation to solve for the diameter of the mega-cone:
(Diameter of mega-cone)³ = (Diameter of mini-cone)³ / Ratio
Substituting the known values:
(Diameter of mega-cone)³ = (2 inches)³ / 0.094
Taking the cube root of both sides:
Diameter of mega-cone = (8 inches / 0.094)^(1/3)
≈ 3.54 inches
Therefore, the diameter of the mega-cone at its widest point is approximately 3.54 inches.