Question

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?

Answer 1

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Answer:

18.8 cubic inches

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.