Question

A right rectangular prism has length 9 cm, width 5 cm, and height 3 cm. If the length, width, and height are doubled, what happens to the surface area?
The surface area is multiplied by 8.

The surface area is multiplied by 4.

The surface area is multiplied by 6.

The surface area is doubled.

Answer 1

The third one is the answer I got it right on the quiz

Answer 2

Answer:

B - The surface area is multiplied by 4.

Step-by-step explanation:

The first step is to figure out the original surface area of the shape using this formula;

A = 2(wl + hl + hw)

Which in this problem, means:

A = 2 (5 × 9) + 2 (3 × 9) + 2 (3 × 5) = 174.

Now, we must figure out the surface area once the measurements are doubled, using the same equation:

A = 2 (10 × 18) + 2 (6 × 18) + 2 (6 × 10) = 696.

If we then take a look back at the original surface area, we can already tell the answer is not D, as 696 is too high to be double 174, considering 150 × 2 is 300, and 24 × 2 is 28.

We can also eliminate option A, as it's clear multiplying 174 by 8 would take us into the thousands, since 8 × 100 is 800, and already over our target.

So we're left with two options - Multiplied by 4, or multiplied by 6.

If we know that multiplying 174 by 8 would take our answer into the thousands, it's also safe to assume multiplying by 6 would do the same, because 6 × 100 is 600, and multiplying 74 by 6 would take us way over target, too.

However, just to be on the safer side, we can divide 696 by 6;

696 ÷ 6 = 116.

Now we have eliminated answer C.

So the answer is B - The surface area is multiplied by 4.

(Confirmation -

696 ÷ 4 = 174

174 × 4 = 696)

Hope this helped!