The surface area of a rectangular prism is 10.4 in2. What is the surface area of a similar prism that is larger by a scale factor of 3?

I am tearing my hair out over this question! Please help asap!

The surface areas of similar solids is proportional to the square of their sides

since the ratio of sides is 1 : 3
their surface areas have the ratio 1^2 : 3^2 or 1 : 9
so the surface area is 9(10.4) or 93.6

or

original width = x
original length = y
original heigt = z
original surface area = 2(xy) + 2(xz) + 2(yz)
= 2(xy + xz + yz)

new width = 3x
new length = 3y
new height = 3z
new surface area = 2(9xy) + 2(9xz) + 2(9yz)
= 18(xy + xz + yz)

ratio of new to old = 18(xy + xz + yz) : 2(xy + xz + yz)
= 9 : 1

Sure! I'd be happy to help you with this math problem.

To find the surface area of the larger prism, we need to know the ratio of the surface areas of the similar prisms. Since the larger prism has a scale factor of 3 compared to the original prism, the ratio of their surface areas is equal to the square of the scale factor (which is 3).

So, let's call the surface area of the original prism SA1 and the surface area of the larger prism SA2. We have the equation:

SA2 = SA1 x (scale factor)^2

The surface area of the original prism, SA1, is given as 10.4 in^2. Therefore, we can plug in these values into the equation:

SA2 = 10.4 in^2 x (3)^2

Calculating the expression inside the parentheses first, we have:

SA2 = 10.4 in^2 x 9

Now, multiply the surface area of the original prism (10.4 in^2) by 9:

SA2 = 93.6 in^2

Therefore, the surface area of the larger prism is 93.6 square inches.

Remember, to find the surface area of the larger prism, we used the ratio of the scale factor squared and then multiplied it by the surface area of the original prism.