Volume word problems with cones, cylinders, and spheres

The  exercise appears under the 8th Grade Math Mission. This exercise uses geometric volume formulas to solve word problems.

Types of Problems
There are four types of problems in this exercise:


 * 1) Use the volume of a cone: This problem describes a word problem that relies on the volume of a cone. The student is asked to find the correct answer and write it in the space provided.Vwpwccas2.png
 * 2) Use the volume of a cylinder: This problem describes a word problem that relies on the volume of a cylinder. The student is asked to find the correct answer and write it in the space provided.Vwpwccas1.png
 * 3) Use the volume of a sphere: This problem describes a word problem that relies on the volume of a sphere. The student is asked to find the correct answer and write it in the space provided.
 * 4) Use the volumes of various geometric solids: This problem calls upon some combination of cone, cylinder and sphere formulas to solve a problem.Vwpwccas4.png

Strategies
Knowledge of the volume formulas can be considered vital to performing this problem accurately and efficiently.
 * 1) The volume of a cone is 1/3*pi*r^2*h.
 * 2) The volume of a cylinder is pi*r^2*h, the volume of the cone multiplied by three.
 * 3) The volume of a sphere is 4/3*pi*r^3.

Real-life applications

 * 1) Volume formulas are useful in the calculus for understand some of the beginning integral applications.
 * 2) Spheres are common shapes in nature when gravity is allowed to act freely (planets, raindrops, etc.)