Practice Scaling in Space in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

Double the size: length \times 2, area \times 4, volume \times 8.

easy

A square has side length 3 cm. If all lengths are doubled (scale factor k=2), what are the new perimeter and area?

medium

A sphere has radius 2 cm and volume V = \frac{4}{3}\pi r^3. If the radius is tripled, how many times larger is the new volume?

easy

A photo is 4 in × 6 in. It is enlarged with scale factor k = 3. What are the new dimensions and new area?

hard

Two similar pyramids have heights 4 m and 10 m. If the smaller pyramid has volume 32 m³, what is the volume of the larger?