Question 1 Here is the base of a prism.

a. If the height of the prism is 5 cm, what is its surface area? What is its volume?

b. If the height of the prism is 10 cm, what is its surface area? What is its volume?

c. When the height doubled, what was the percent increase for the surface area? For the volume?

a ) Surface Area ⇒ 222 cm^2, Volume ⇒ 180 cm^3

b ) Surface Area ⇒ 372 cm^2, Volume ⇒ 360 cm^3

c ) Surface Area Increase ⇒ ( About ) 67.56 %, Volume Increase ⇒ 100 %

Step-by-step explanation:

a ) Consider dividing the figure into parts, first solving for the area of the base, using the attachment below for guidance;

As you can see, in the picture I have made it so that the base is nested in a rectangle with dimensions 8 by 5. Calculating the area of this rectangle, subtracting the area of a square with dimensions 2 by 2 cm, we can derive the area of the base in a much quicker manner;

Now let us imagine adding the another dimensions to this two dimensional base. That would make a 3 - d prism, with surface area equivalent to mini rectangles and squares with a common dimension being the length of the height; 5 cm

b ) We have calculated the area of the base before, now let us solve for all the " mini shapes " given a new height of 10 cm;

c ) Solution; Increase of Surface Area ⇒ ( About ) 67.56 %, Increase of Volume ⇒ 100 %

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step-by-step explanation: