Surface Area and Volume please help guys!

Question

A prism has total surface area of 360m^2 and volume of 60m^3

If the length, width, and height are reduced to half their original sizes, what will be the following?

a) the new surface area

b) the new volume

If the length, width, and height of the original are increased to triple their original sizes, what will be the following?

c) the new surface area

d) the new volume

please show work for all

Answer 1

(1a)

The total surface area of the prism is .

The length, width and height are reduced to half their original size.

Surface area of the prism is .

Here is the base,

is the height of the base triangle,

is the perimeter .

is the height of the prism.

If the length, width and height are scaled by a factor of  then surface area of the prism is scaled by a factor of .

Surface area of the prism:

If the length, width, and height are reduced to half their original size then surface area of the prism is

Answer 2

(1b)

The volume of the prism is .

The length, width and height are reduced to half their original size.

The length, width and height are scaled by a factor of .

Volume of the prism is .

Here is the base,

is the height of the triangle and

is the height of the prism.

If the length, width and height are scaled by a factor of then volume of the prism is scaled by a factor of .

Volume of the prism:

If the length, width, and height are reduced to half their original size then surface area of the prism is .

Answer 3

(1c)

The total surface area of the prism is .

The length, width and height are increased to triple their original size.

Therefore the length, width and height are scaled by a factor of .

If the length, width and height are scaled by a factor of  then surface area of the prism is scaled by a factor of .

Surface area of the prism:

If the length, width, and height are increased to triple their original size then surface area of the prism is

Answer 4

(1d)

The volume of the prism is .

The length, width and height are increased to triple their original size.

Therefore the length, width and height are scaled by a factor of .

If the length, width and height are scaled by a factor of  then volume of the prism is scaled by a factor of .

Volume of the prism:

If the length, width, and height are increased to triple original size then surface area of the prism is .