Two cones are displayed. The smaller cone to the left is labeled 'r equals 8 feet' and the slant height is labeled '12 feet.' The larger cone to the right is labeled below with an x and the slant height is labeled '15 feet.'

Question

What is the length of the radius of the larger cone?
A. 10 ft
B. 11 ft
C. 12 ft
D. 13 ft

Answer 1

We can use the formula for the slant height of a cone: $l=\sqrt{r^2+h^2}$, where $r$ is the radius and $h$ is the height. We can set up an equation using this formula for each cone:
For the smaller cone: $12=\sqrt{8^2+h^2}$
Solving for $h$, we get $h=4\sqrt{5}$
For the larger cone: $15=\sqrt{x^2+h^2}$
Substituting the value we found for $h$, we get $15=\sqrt{x^2+80}$
Squaring both sides gives $225=x^2+80$
Solving for $x$, we get $x=\pm 13$
Since $x$ represents a length, we take the positive value, so the radius of the larger cone is $\boxed{\textbf{(D)}\ 13 \ \text{ft}}$.

Answer 2

assuming the cones are similar (otherwise there is no way to determine x),
x/8 = 15/12
x = 10
so, A

Answer 3

This solution is incorrect as there is no given information that states the cones are similar.