Sometimes, you need to use subtraction to solve a volume problem.

Description: Sphere with diameter

A box is needed to ship a signed youth soccer ball from the Houston Dynamos to a fan in Mission, Texas. The ball can NOT move around in the box, therefore it is important to find the smallest shipping box possible and the amount of space remaining to put filler in before shipping the soccer ball. The ball has a diameter of 8 inches. How much filler material will need to be shipped with the ball so that it does not move around in the box?

  1. WhatInteractive popup. Assistance may be required. shape A cubeClose Pop Up box will be the smallest box to fit around a spherical soccer ball?
  2. Determine the volume of the soccer ball. Identify theInteractive popup. Assistance may be required. formula V = 4 3 πr3Close Pop Up for the volume of the sphere.
  3. Do you have all of theInteractive popup. Assistance may be required. dimensions We are given the diameter, and we need to know the radius. The radius is half the length of the diameter. Close Pop Up that you need? If not, how can you determine those dimensions?
  4. Now, you can find theInteractive popup. Assistance may be required. volume of the sphere V = 4 3 πr3
    4 3 π(4 inches)3
    ≈ 268 in3     Close Pop Up     .
  5. Determine the volume of the box. Identify theInteractive popup. Assistance may be required. formula V = s3Close Pop Up . Do you have all of theInteractive popup. Assistance may be required. dimensions We indirectly know that the edge length of the cube is equal to the diameter of the sphere.Close Pop Up that you need? If not, how can you determine those dimensions?
  6. Find theInteractive popup. Assistance may be required. volume of the cube V = s3
    = (8 inches)3
    = 512 in3    Close Pop Up     .
  7. Find the Interactive popup. Assistance may be required. difference of the volumes Vfiller = Vbox - Vball
    V = Vcube - Vsphere
    ≈ 512 in3 - 268 in3
    ≈ 244 in3 Close Pop Up     of the two 3-dimensional figures.