I need help to solve:
A cylinder with radius 4 cm and perpendicular height 15 cm is tilted so that it will just fit inside a 12 cm high box. At what angle must it be tilted?
Answer given at the back of the text book is 16 degrees 15 minutes.
Hello, lalji!
I don't agree with their answer . . .
A cylinder with radius 4 cm and perpendicular height 15 cm
is tilted so that it will just fit inside a 12 cm high box.
At what angle must it be tilted?
Answer given: 16 degrees 15 minutes.Code:P A S _ * - - - * - - - - * : | * * | : | * *D | : | * * | 12-x| * 15 * | : | * * | : | * * | : |* * | -B* 8 * | x | * * | - * - - * - - - - - * Q C R
The cylinder is
The box is
Let
Let
. . Note that
In right triangle
. .
In right triangle
. .
Equate [1] and [2]: .
Square both sides: .
. . which simplifies to: .
. . and has the positive root: .
Then: .
. .
When I saw this question, I knew I saw it before. It was in my textbook last year. Here is the picture the book provided, and the answer at the back of the book is 16 degrees 50 minutes, not 16 degrees 15 minutes. I think Soroban had a correct answer, but the book is asking for the angle of the other side. So:
(straight angle) - (angle between base and length of cylinder) - (angle 'on the other side' Soroban found) =
=