The cones below are similar, although not drawn to scale.
Two cones are displayed. The smaller cone to the left is labeled 'r equals 6 feet' and the slant height is labeled '18 feet.' The larger cone to the right is labeled below with an x and the slant height is labeled '27 feet.'
What is the length of the radius of the larger cone?
A. 4 ft
B. 6 ft
C. 9 ft
D. 12 ft
We can use the fact that the cones are similar to set up a proportion between the corresponding sides. The ratio of the radii should be the same as the ratio of the slant heights:
r1 / 18 = r2 / 27
where r1 is the radius of the smaller cone (6 feet) and r2 is the radius of the larger cone (unknown).
We can solve for r2 by cross-multiplying and simplifying:
r2 = r1 * 27 / 18
r2 = 6 * 27 / 18
r2 = 9
Therefore, the length of the radius of the larger cone is 9 feet.
The answer is C. 9 ft.