Question

A cube has an edge length of 3 inches.

a) Find the surface area and volume of the cube.

b) The cube is dilated by a scale factor of 0.5.
Find the surface area and volume of the image.

PLEASE HELP THIS IS DUE TOMORROW!!!

Answer 1

Question (a)

Surface area of a cube =
`6x^2` (where
`x` is an edge length)

⇒ surface area = 6 × 3²

= 6 × 3 × 3

= 6 × 9

= 54 in²

Volume of a cube =
`x^3` (where
`x` is an edge length)

⇒ volume = 3³

= 3 × 3 × 3

= 27 in³

Question (b)

To find the area of a dilated figure, simply multiply the original area by the scale factor squared:

Surface area =
`6x^2` × sf²

= 54 × 0.5²

= 13.5 in²

To find the volume of a dilated figure, simply multiply the original volume by the scale factor cubed:

Surface area =
`x^3` × sf³

= 27 × 0.5³

= 3.375 in³