Question

If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area

Answer 1

SA=2(LW+LH+WH)
if W turns to 1/7W
and H turns to 1/7H
SA=2(L(1/7)W+L(1/7)H+(1/7)W(1/7)H)
SA=2((1/7)LW+(1/7)LH+(1/49)WH)
SA=2(1/7)(LW+LH+(1/7)WH)
SA=(2/7)(LW+LH+(1/7)WH)

Answer 2

SA =
`2((lw)/(7)+(lh)/(7)+(wh)/(49))`

Explanation:

The surface area of a rectangular prism is given by :

`SA=2(wl+hl+hw)`

Where l stands for length

w stands for width

h stands for height

Given is - If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same.

So, length = l

width =
`(w)/(7)`

height =
`(h)/(7)`

The new surface area will be =

SA =
`2(l* (w)/(7) +l* (h)/(7)+ (w)/(7)* (h)/(7))`

Simplifying this we get:

SA =
`2((lw)/(7)+(lh)/(7)+(wh)/(49))`

There are many other ways to write this but it has the same meaning, so, we can take this as the answer.

SA =
`2((lw)/(7)+(lh)/(7)+(wh)/(49))`