SOLUTION: The radius of the base of each of two right circular cones is 8 inches. The altitude of the first cone is 9 greater than that of the second cone and its slant height is 7 inches gr
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Question 900733: The radius of the base of each of two right circular cones is 8 inches. The altitude of the first cone is 9 greater than that of the second cone and its slant height is 7 inches greater than that of the second. Find the altitude of the taller cone.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The radius of the base of each of two right circular cones is 8 inches.
The altitude of the first cone is 9 greater than that of the second cone
and its slant height is 7 inches greater than that of the second.
Find the altitude of the taller cone.
:
This can be done by considering two right triangles, using pythag formulas
let x = the height of taller cone
then
(x-9) = the height of the smaller cone
The slant dimensions are the hypotenuses
- 7 =
- 7 =
- 7 =
square both sides
subtract x^2 from both sides
simplify, change the signs, divide by -2
square both sides
49(x^2 + 64) = 81x^2 - 288x + 256
49x^2 + 3136 = 81x^2 - 288x + 256
combine like terms on the right
0 = 81x^2 - 49x^2 - 288x + 256 - 3136
0 = 32x^2 - 288x - 2880
simplify divide by 32
x^2 - 9x - 90 = 0
Factors to
(x-15)(x+6) =
the positive solution here
x = 15 in is the altitude of the taller cone
:
:
See if that checks out the height of the smaller will be 6
= 17
= 10
----------------------
slant differences 7 in
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