+354 A cylinder is 48 cm high and has a circumference of 16cm. A piece of string makes 4 coils around the cylinder from top to bottom. What is the length of the string?
+23252 CPhill:
If you had the string go from the upper-left corner to the lower-right corner and then twisted the sheet into a cylinder, wouldn't the string just wrap around once?
To wrap around four times, wouldn't you have to go from the upper-left corner to one-fourth of the way down the right side and then repeat that three more times?
For one-fourth of the way, width = 16 and height = 12:
√( 16² + 12²) = 20
For four times around: 20 x 4 = 80 cm.
+129850 This one seems difficult...but it's not that hard.....
If we unroll the cylinder we have a rectangle that is 48cm high and 16cm wide. And the string would extend from one bottom edge of the rectangle to the opposite top corner. Thus, the string is the hypoteneuse of a right triangle with legs of 48 and 16. And the string's length is given by.....
√(48^2 + 16^2) = √2560 ≈ 50.6 cm
I think that's it ......???
+23252 CPhill:
If you had the string go from the upper-left corner to the lower-right corner and then twisted the sheet into a cylinder, wouldn't the string just wrap around once?
To wrap around four times, wouldn't you have to go from the upper-left corner to one-fourth of the way down the right side and then repeat that three more times?
For one-fourth of the way, width = 16 and height = 12:
√( 16² + 12²) = 20
For four times around: 20 x 4 = 80 cm.
