Part 1: Doubling and Tripling

A rectangular prism has each side doubled.Watch the video below to see how this will effect the surface area and volume of the rectangular prism.

https://youtu.be/XInrsVZzgx4

(A) Complete the statement:

When each side of a rectangular prism is doubled, the surface area becomes____ times larger and the volume becomes ____ times larger.

(B) Show what happens to surface area and volume if similar doubling is done to dimensions in each of the following solids.Make sure you use general terms as demonstrated in the video.

(i) Cylinder (radius and height doubled):

(ii) Cone (radius and height doubled):

(iii) Pyramid (base edges and height doubled):

(iv) Sphere (radius doubled):

(C) Based off of the results above, complete the following statement:

When each dimension of a solid is doubled, the surface area becomes____ times larger and the volume becomes ____ times larger.

(D) Based on the observations above, or by using similar observations, complete the following statement:

When each dimension of a solid istripled, the surface area becomes____ times larger and the volume becomes ____ times larger.

Show all work that leads to your conclusion.

Part 2: Other Factors Complete the following statements. Give explanations or show work that justifies the statements you make like you did in part 1. (A) When each dimension ofa solid is multiplied by 4, the surface area becomes times larger and the volume becomes times larger. (5) When each dimension ofa solid is multiplied by 5, the surface area becomes times larger and the volume becomes times larger. (C) When each dimension of a solid is multiplied by 1, the surface area becomes times smaller and the volume becomes 2 times smaller. (D) When each dimension ofa solid is multiplied by 1, the surface area becomes times smaller and the volume becomes 3 times smaller. (E) When each dimension of a solid is multiplied by r, the surface area would be equal to times the original surface area and the volume equal to times the original volume. Part 3: Use What You Learned The statue shown below is a model of one that is going to be built in a nearby park. This model required 256 cubic inches of concrete to make. If the actual statue is to be the exact same shape but each dimension is 2 feet for each inch in dimension for the model, how many cubic feet of concrete will be needed to create the statue