a company makes two different-sized ice cream cones. The smaller cones are 3.5 inches tall and have a diameter of 3 inches. The larger cones are 5.1 inches tall and have a diameter of 4.5. inches. About how much greater, to the nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone?

9514 1404 393

  18.8 cubic inches

Step-by-step explanation:

The formula for the volume of a cone is useful:

  V = 1/3πr²h

Where r is half the diameter, we can use r=d/2 to write this in terms of diameter:

  V = 1/3π(d/2)²h = (π/12)d²h

For the given dimensions, the volumes are ...

  large cone: v = (π/12)(4.5 in)²(5.1 in) ≈ 27.04 in³

  small cone: v = (π/12)(3 in)²(3.5 in) ≈ 8.25 in³

Then the difference in volume is ...

  (27.04 -8.25) in³ ≈ 18.8 in³

The larger cone has about 18.8 cubic inches more volume.