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Geometry Question Help?
For a right circular cone the ratio of the slant height to the radius is 5:3 if the volume of the cone is 96 pie inches cubed. find the lateral area of the cone
the answer the book is giving me is 60pie
i can't see the pattern to solving this, can anyone give me step by step instructions.
1 Answer
- 8 years agoFavorite Answer
V = (1/3) * pi * r^2 * h
A = pi * r^2 + pi * r * s
s = sqrt(r^2 + h^2)
s/r = 5/3
3s = 5r
3 * sqrt(r^2 + h^2) = 5r
9 * (r^2 + h^2) = 25r^2
9r^2 + 9h^2 = 25r^2
9h^2 = 16r^2
3h = 4r
h = (4/3) * r
V = (1/3) * pi * r^2 * h
96 * pi = (1/3) * pi * r^2 * (4/3) * r
96 = (4/9) * r^3
96 * (9/4) = r^3
24 * 9 = r^3
216 = r^3
6 = r
h = (4/3) * r
h = (4/3) * 6
h = 8
Lateral area is the area of the cone minus the base
A = pi * r * s
A = pi * r * sqrt(r^2 + h^2)
A = pi * 6 * sqrt(6^2 + 8^2)
A = pi * 6 * sqrt(100)
A = pi * 6 * 10
A = 60pi