Scaling in Space Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

A photo is 4 in × 6 in. It is enlarged with scale factor

k = 3

. What are the new dimensions and new area?

1
Step 1: New dimensions: $4 \times 3 = 12$ in and $6 \times 3 = 18$ in.
2
Step 2: New area: $12 \times 18 = 216$ in², or equivalently: original area $24$ in² $\times 3^2 = 24 \times 9 = 216$ in².

Answer

New dimensions:

12

\times

18

in; new area:

216

in².

Scaling a rectangle by

k

scales each side by

k

and the area by

k^2

. The original area was

4 \times 6 = 24

in², and

24 \times 9 = 216

in².

About Scaling in Space

How length, area, and volume measurements change when a figure is uniformly enlarged or shrunk by a scale factor.

A square has side length 3 cm. If all lengths are doubled (scale factor [formula]), what are the new

A sphere has radius 2 cm and volume [formula]. If the radius is tripled, how many times larger is th

Two similar pyramids have heights 4 m and 10 m. If the smaller pyramid has volume [formula] m³, what