Question

PLEASE HELP!!!!

Mike says that if he doubles each dimension of any rectangular prism, the surface area also doubles. Is Mike correct? Give an example to support your answer.

Answer 1

Mike is not right

Explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the enlarged rectangular prism

y-----> surface area of the original rectangular prism

`z^(2)=(x)/(y)`

so

In this problem we have

`z=2`

substitute

`2^(2)=(x)/(y)`

`4=(x)/(y)`

`x=4y`

so

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism

therefore

Mike is not right

Verify with an example

we have a rectangular prism

`L=5\ m`

`W=2\ m`

`H=3\ m`

The surface area of the prism is equal to

`SA=2(LW)+(2L+2W)H`

substitute the values

`SA=2*(5*2)+(2*5+2*2)*3=62\ m^(2)`

If he doubles each dimension of any rectangular prism

then

the new dimensions will be

`L=5*2=10\ m`

`W=2*2=4\ m`

`H=3*2=6\ m`

The new surface area will be

`SA=2*(10*4)+(2*10+2*4)*6=248\ m^(2)`

`248/62=4`

therefore

The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism