Question

Jake stores a small cache of 4-inch-diameter snowballs in the basement freezer, unaware that the freezer’s self-defrosting feature will cause each snowball to lose about 1 cubic inch of volume every 40 days. He remembers them a year later (call it 360 days) and goes to retrieve them. What is their diameter then?

Answer 1

The diameter of the snowballs after one year is approximately 3.66 inches.

Step-by-step explanation:

To find the diameter of the snowballs after one year, we need to determine how much volume they have lost. Since each snowball loses 1 cubic inch of volume every 40 days, we can calculate the total volume loss over 360 days. There are 9 intervals of 40 days in 360 days, so the snowballs would have lost 9 cubic inches of volume. The volume of a sphere with diameter d can be calculated using the formula V = (4/3)π(r^3), where r is the radius (half the diameter). We know that the original diameter is 4 inches. Let's solve for the diameter:

V = (4/3)π(r^3)

9 = (4/3)π((d/2)^3)

9 = (4/3)π(d^3/8)

3 = π(d^3/8)

d^3/8 = 3/π

d^3 = 24/π

d = (24/π)^(1/3)

Using a calculator, we find that the diameter is approximately 3.66 inches.