Chapter 12, Problem 11CT

To determine

To check:Whether the cone are similar or not.

Answer to Problem 11CT

The two cones are not similar.

Explanation of Solution

Given information:

The radii of two cones are $12\text{cm}$ and $18\text{cm}$ and the slant height of two cones are $18\text{cm}$ and $24\text{cm}$ .

Calculation:

Let $r_1$ and $r_2^{}$ are radius of two cones,and $l_1$ and $l_2$ are slant height of the two cones.

For cones to be similar, then ratio of radii and ratio of slant height of two cones must be same.

  $\frac{r_1}{r_2}=\frac{l_1}{l_2}$

Calculate the ratio of radii of two cones

  $\begin{array}{c}\frac{r_1}{r_2}=\frac{12}{18}\\ =\frac{2}{3}\end{array}$

Calculate the ratio of slant height of two cones.

  $\begin{array}{c}\frac{l_1}{l_2}=\frac{18}{24}\\ =\frac{3}{4}\end{array}$

From the above, it is clear that the ratio of radii and the ratio of slant height of two cones are not same.

Therefore,the two cones are not similar.