We know the heights of two similar cones but the radius and slant height of just one of them.
Recall that similar solids are solids that have the same shape and proportional corresponding dimensions. Therefore, the ratio between corresponding dimensions is constant. We can use this information to write a proportion. We want to find the value of l and r. Let's do this one at time.
Value of l
We know that a cone with a slant height of 3 inches and a height of 3.4 inches is similar to a cone with a slant height of l and a height of 4.5 inches.
Height of bigger cone/Height of smaller cone
=
Slant height of bigger cone/Slant height of smaller cone
Let's substitute the corresponding dimensions into this equation and solve for l.
Height of bigger cone/Height of smaller cone=Slant height of bigger cone/Slant height of smaller cone
The slant height of the bigger cone l is 5.1 inches.
Finding r
We know that a cone with a radius of 1.6 inches and a height of 3.4 inches is similar to a cone with a radius of r and a height of 4.5 inches.
Height of bigger cone/Height of smaller cone
=
Radius of bigger cone/Radius of smaller cone
Let's substitute the corresponding dimensions into this equation and solve for r.
Height of bigger cone/Height of smaller cone=Radius of bigger cone/Radius of smaller cone
