Question 958126: A prism has a surface area of 350 mm2.
Find the surface area of a scaled image with a scale factor of 2.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! surface area is the sum of the areas of each face.
if you double the dimensions, you quadruple the area.
if the surface area is 350 mm^2, and the scale factor is 2, then the surface area will be quadrupled to 1400 mm^2.
for example:
let a rectangular prism have a length of L and a width of W and a height of H.
The surface area of the prism will be:
(2 * L * W) + (2 * L * H) plus (2 * W * H).
if the scale factor is 2, then each dimension is multiplied by a factor of 2.
the surface area of the scaled prism will then be:
(2 * 2 * L * 2 * W) + (2 * 2 * L + 2 * H) plus (2 * 2 * W * 2 * H).
simplify that equation and you get:
the surface area of the scaled prism will be:
(8 * L * W) + (8 * L * H) + (8 * W * H).
The surface area went from 2 * the area of each face to 8 * the area of each face.
That's a scale factor of 8 / 2 = 4.
4 is equal to 2^2.
The scale factor of the surface area is equal to the square of the scale factor of the dimensions.
|
|
|
