Tripling Surface Area of Rectangular Prism-8th grade

[Chels13]

Hi, I have a test tomorrow & I'm trying to get through the study guide. The problem is:

The surface area of a rectangular prism is 298 square units. If the dimensions are tripled, what is the surface area of the figure in square units?

I originally multiplied 298 * 3, which ='s 894, but that's wrong. Is there a formula I can use or something?

On another problem, it asks:

If the perimeter of a rectangular prism is 420 cubic units, what is its perimeter if the dimensions are reduced to one-third their original length?I'm not sure if I answered it correctly or not. I put 140 as the answer. My work is 420 cubic units; sf = 1/3, so 420/3 = 140. Is that right?


Thanks!

 

[royhaas]

You are correct about the perimeter, because perimeter is measured in linear units. However, area is measured in square units. If you increase each dimension by a factor of \(\displaystyle 3\), then the area is increased by a factor of \(\displaystyle 3^2\).

 

[Chels13]

Yay! Thanks. And so if I do 3 squared..would it be 298 times 3 which is 894, times 3 again?

(2,682)

 

[mmm4444bot]

Yes. (9) (298) = 2682

Think of a cube; each side has length x.

The surface area of one side is x^2.

There are six sides, all the same.

Total surface area is 6 * x^2.

6x^2 = 298

Now, triple the side length to 3x.

Total enlarged surface area is 6 * (3x)^2

(6) (3^2) (x^2) = (9)(6x^2)

Since 6x^2 equals 298, the total enlarged surface area is 9 times 298.

On your second exercise, 2L + 2W = 420.

Reduce each dimension to 1/3.

2(L/3) + 2(W/3)

Factor out the 1/3.

(1/3) (2L + 2W) = (1/3) (420) = 140

 

[Deleted member 4993]

Hi, I have a test tomorrow & I'm trying to get through the study guide. The problem is:

The surface area of a rectangular prism is 298 square units. If the dimensions are tripled, what is the surface area of the figure in square units?

I originally multiplied 298 * 3, which ='s 894, but that's wrong. Is there a formula I can use or something?

On another problem, it asks:

If the perimeter of a rectangular prism is 420 CUBIC units --- Are you sure this is correct? - if it is then the problem is WRONG, what is its perimeter if the dimensions are reduced to one-third their original length?I'm not sure if I answered it correctly or not. I put 140 as the answer. My work is 420 cubic units; sf = 1/3, so 420/3 = 140. Is that right?


Thanks!