Similar Figures Math Example 4

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

Example 4

medium

Two similar cones have base radii

3

cm and

7

cm. What is the ratio of their volumes?

Solution

1
Linear scale factor: $k = \dfrac{7}{3}$ .
2
Volumes scale by $k^3$ : ratio $= \left(\dfrac{7}{3}\right)^3 = \dfrac{343}{27}$ .

Answer

Volume ratio is

\dfrac{343}{27}

For similar 3D figures with linear scale factor

k

, volumes scale by

k^3

. A relatively modest change in linear size produces a dramatically larger change in volume, which is why this cubic relationship is important to remember.

About Similar Figures

Similar figures have the same shape with corresponding angles equal and corresponding sides proportional.

Learn more about Similar Figures →

More Similar Figures Examples

Example 1 easy

Two similar triangles have corresponding sides [formula] cm and [formula] cm. If the smaller triangl

Example 2 hard

Rectangle [formula] Rectangle [formula] with [formula], [formula], [formula]. Find [formula] and the

Example 3 easy

Triangle [formula] Triangle [formula]. [formula], [formula], [formula]. Find [formula].

Related Concepts

Similarity Proportions Scale Drawings