Solid geometry

The Solid geometry exercise appears under the 8th grade (U.S.) Math Mission and the High school geometry Math Mission. This exercise has practice with various surface area and volume concepts on three-dimensional objects.

Types of Problems

There are two types of problems in this exercise:

1. Find the surface area: This problem provides a manipulative of a three-dimensional object. The user is asked to find the (total) surface area of the object and write it in the space provided.

   

   Find the surface area

2. Find the volume: This problem provides a manipulative of a three-dimensional object. The user is asked to find the volume of the object and write it in the space provided.

   

   Find the volume

Strategies

Knowledge of surface area and volume concepts are necessary to do this exercise, and knowing the formulas helps to perform it more mechanically.

1. In general, volume of a prism is the area of a base multiplied by the height of the object.
2. In general, surface area of a prism is the perimeter of the base multiplied by the height of the prism, plus the area of two bases.
3. The cube occurs often. The volume of a cube is $s^3$ and it's surface area is $6s^2$.

Real-life applications

1. Surface area is used to make packaging for many things in the store, such as boxes and bottles.
2. Volume is used to understand how much certain containers can hold for transportation or possibly artistic purposes.