Question

1. Discuss the differences between the measurement of the surface area and the measurement of the volume of a right rectangular prism. Include the following topics in your discussion.

(a) Description of regions that are measured
(b) Units for each type of measure and why the units are different
(c) Examples of when you would want to measure for each type of measure

Answer 1

Given:
Right Rectangular Prism.
It has its length, width, and height.

Surface area of a right rectangular prism has this formula:
SA = 2 (wl + hl + hw)

Volume of a right rectangular prism has this formula
V = whl

Formula of Surface Area is different from Volume.

Surface area measures the area the whole rectangular prism surface. It computes for the area of all 6 faces that a right rectangular prism has.

Volume measures the area within the rectangular prism. It is the space that is enclosed within the rectangular prism.

Answer 2

For this case we have a rectangular prism.

The area is given by:

`image`

The volume is given by:

`image`

Where,

w: width

h: height

l: length

Part A:

The regions that are measured when we calculate the area are all the faces of the rectangular prism.

The regions that are measured when we calculate the volume are all the dimensions of the rectangular prism.

Part B:

Area: units ^ 2

Volume: units ^ 3

Part C:

Area: We want to calculate the amount of paint needed to paint a wooden box on the outside.

Volume: We want to calculate the amount of water inside a rectangular tank