Two cones are similar. The surface area of the larger cone is 65π square inches. The surface area of the smaller cone is 41.6π s

Question

2 years ago

8

quare inches. The radius of the smaller cone is 6.4 inches. What is the radius of the larger cone? 8 inches 10 inches 11.52 inches 14.4 inches

2 answers:

alekssr [168] · Answer 1 · 2023-03-24T15:34:34+03:00

6 0

Answer:

8

Step-by-step explanation:

Ed2020

devlian [24] · Answer 2 · 2023-03-24T14:34:24+03:00

Answer:

8 inches

Step-by-step explanation:

The surface area of a cone (without the base) is given by:

Surface area = pi*r*s

Where r is the base radius and s is the slant height.

The smaller cone has a surface area of 41.6pi in2 and a radius of 6.4 inches, so the slant height is:

41.6pi = pi*r*s

41.6 = 6.4s

s = 6.5 in

If the cones are similar, the radius and the slant height increase in the same proportion, so we have that:

r'/s' = r/s = 6.4/6.5

s' = r'*6.5/6.4

So for the larger cone, we have:

65pi = pi*r'*s'

65 = r'*r'*6.5/6.4

r'^2 = 64

r' = 8 inches