Question

Question 1

Answer 1

Answer:

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;

$Area of Base - ( 8 cm * 5 cm ) - ( 2 cm* 2 cm ) = 40 square cm - 4 square cm = \\Solution; Base = 36 square cm$

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

$Area of 1 Square = 5 cm * 5 cm = 25 square cm,\\Area of 2 Square = 25 square cm,\\Area of 1 Rectangle = 3 cm * 5 cm = 15 square cm,\\Area of 2 Rectangle = 15 square cm,\\Area of 3 Rectangle = 2 cm * 5 cm = 10 square cm,\\Area of 4 Rectangle = 10 square cm,\\Area of 5 Rectangle = 10 square cm,\\Area of 6 Rectangle = 8 cm * 5 cm = 40 square cm\\Area of Base 2 = 36 square cm,\\\\Surface Area of Figure = 25 + 25 + 15 + 15 + 10 + 10 + 10 + 40 + 36 + 36 = 222 square cm\\Volume = 36 square cm * 5 cm = 180cubiccm$

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;

$Area of Rectangle 1 = 5 cm * 10 cm = 50 cm^2,\\Area of Rectangle 2 = 50 cm^2,\\Area of Rectangle 3 = 3 cm* 10 cm = 30 cm^2,\\Area of Rectangle 4 = 30 cm^2,\\Area of Rectangle 5 = 2 cm * 10 cm = 20 cm^2,\\Area of Rectangle 6 = 20 cm^2,\\Area of Rectangle 7 = 20 cm^2,\\Area of Rectangle 8 = 8 cm * 10 cm = 80 cm^2,\\\\Surface Area of Figure = 50 + 50 + 30 + 30 + 20 + 20 + 20 + 80 + 36 + 36 = 372 cm^2\\Volume of Figure = 36 cm^2 * 10 cm = 360 cubic cm$

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