f) As flour is poured onto a table it forms a right circular cone. The lateral surface area of this cone is described by the formula:
L=(pie)R SquarRoot R^2+H^2
where L is the lateral surface area,
R is the radius of the base of the cone
H is the height of the cone
If the height of the cone is 4 inches and the lateral surface area is 15 square inches,
find the radius of the cone. ?
2007-12-01 08:38:40 · 1 answers · asked by Curtis N 2 in Science & Mathematics ➔ Mathematics
L= 15(pie)^2
2007-12-02 08:01:11 · update #1
L=15(pie)^2
H=4
R=?
2007-12-02 08:02:28 · update #2
L = πR√(r^2 + H^2)
H = 4, L = 15, R = ?
(L/π)^2 = R^2(R^2 + H^2)
(L/π)^2 = R^4 + R^2H^2
R^4 + R^2H^2 - (L/π)^2 = 0
R^4 + 16R^2 -225/π^2 = 0
Let x = R^2
x^2 + 16x - 225/π^2 = 0
x = [-16 +/- √(16^2 + 4(225/π^2))]/2
x = -8 +/- √(64 + 225/π^2)
x = 1.3165, -17.3165[extraneous]
R^2 = x
R = √x = √1.3165 = 1.1474in.
2007-12-01 14:46:56 · answer #1 · answered by jsardi56 7 · 1⤊ 0⤋