A spherical watermelon has a 12 in. diameter. The volume of a particular sphericalcantaloupe (melon) is21 of the volume of the watermelon. Find the diameter ofthe cantaloupe to the nearest tenth of an inch

The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere.

1. First, we need to find the radius of the watermelon. The diameter is 12 inches, so the radius is half of that, which is 6 inches.

2. Next, we calculate the volume of the watermelon using the formula. V = 4/3 * π * 6³ = 288π cubic inches.

3. The volume of the cantaloupe is 2/3 of the volume of the watermelon. So, the volume of the cantaloupe is 2/3 * 288π = 192π cubic inches.

4. Now, we need to find the radius of the cantaloupe. We can use the volume formula again, but this time we solve for r.

   192π = 4/3 * π * r³

   Simplifying this gives r³ = (192π * 3/4) / π = 144

   Taking the cube root of both sides gives r = ∛144 = 5.2 inches to the nearest tenth.

5. Finally, we find the diameter of the cantaloupe by doubling the radius. So, the diameter of the cantaloupe is 5.2 * 2 = 10.4 inches to the nearest tenth.