The radius and height of a cone are in the ratio 3:4 if its volume is 301.44 cm² what is the radius and height
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Answered by
23
hey there,
r : h = 3 : 4
r = (3/4)h
V = 1/3 (pi) (r^2) (h)
301.44 = 1/3 (pi) (r^2) (h)
(h)(r^2) = 287.854
Substitute r = 3/4 h into the equation
(h)[(3/4 h)^2] = 287.854
h(9/16 h^2) = 287.854
9/16 h^3 = 287.854
h^3 = 511.740
h = 7.99
h = 8
r = 3/4 h
r = 3/4 (8)
r = 6
Slant height = sqrt[h^2 + r^2]
s = sqrt[8^2 + 6^2]
s = sqrt[64 + 36]
s = sqrt(100)
s = 10
Radius = 6 cm
Slant height = 10 cm
Hope this helps!
r : h = 3 : 4
r = (3/4)h
V = 1/3 (pi) (r^2) (h)
301.44 = 1/3 (pi) (r^2) (h)
(h)(r^2) = 287.854
Substitute r = 3/4 h into the equation
(h)[(3/4 h)^2] = 287.854
h(9/16 h^2) = 287.854
9/16 h^3 = 287.854
h^3 = 511.740
h = 7.99
h = 8
r = 3/4 h
r = 3/4 (8)
r = 6
Slant height = sqrt[h^2 + r^2]
s = sqrt[8^2 + 6^2]
s = sqrt[64 + 36]
s = sqrt(100)
s = 10
Radius = 6 cm
Slant height = 10 cm
Hope this helps!
Answered by
15
AnswEr:
Let the radius r and height h of the cone be 3x cm and 4x cm respectively.
Then,
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