8.4 Notes:

Surface Areas and Volumes of Similar Solids

Learning Objective: Use properties of similar solids to solve problems involving surface area and volume.

* Similar solids - solids that have the same shape and proportional corresponding dimensions

Example 1: Which cylinder is similar to Cylinder A?

Example 2: The cones are similar.  Find the missing slant height l

Surface Area of Similar Solids

When two solids are similar, the ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures

Example 3: The pyramids are similar.  What is the surface area of Pyramid A?

Volumes of Similar Solids

When two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

Example 4: The dimensions of the touch tank at an aquarium are doubled.  What is the volume of the new touch tank?

8.4 Practice Problems

1.) The prisms are similar.  Find the missing width and length.

2.) The solids are similar.  Find the surface area of the red solid.  Round your answer to the nearest tenth.