Question

The areas of the bases of two similar conesare in the ratio of 9: 16.(a) Find the ratio of the heights of thecones.(b) Given that the volume of the largercone is 448 cm?, find the volume of thesmaller cone.

Answer 1

79.73 cm³

Step-by-step explanation:

When two figures are similar, the ratio of their measures is constant, so the ratio of the heights of the cones is also

9 : 16

The relation between the volume of the larger cone and the smaller cone is

V1 = k³V2

Where k is the ratio written as a fraction. So, replacing k by 9/16, we get:

`\begin{gathered} V_1=((9)/(16))^3V_2 \\ \\ V_1=((729)/(4096))(448) \\ \\ V_1=79.73 \end{gathered}`

Therefore, the volume of the smaller cone is 79.73 cm³