 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that A can of a drink even the shape of a cylinder with height 17 cm and radius 3.5 cm What is the height of the longest straw that can be fitted inside the can? We know that Pythagoras theorem states in our right angle triangle with hypotenuse c and let a and b we have c square is equal to a square plus b square That is, square of the length of hypotenuse is equal to sum of squares of length of legs with this key idea let us proceed to the solution Now in this question we are given a can in the shape of a cylinder whose radius is 3.5 cm and height is 17 cm And we have to find the height of longest straw that can be fitted inside the can It means we have to find the length of the straw Now we see that the straw can be fitted vertically or slantingly When we fit the straw vertically its length should be equal to the height of the cylinder But the longest straw will be fitted slantingly inside the can Let length of the straw be x cm and we have given height of the cylinder Let us assume it as h is given as 17 cm Also the radius of the cylinder let us name it as r is given as 3.5 cm Here in the figure we have a b at the diameter of the cylinder a c is the height of the straw b c is the height of the cylinder So we have b c that is the height of the cylinder is given as 17 cm And a c we have assumed as x cm and a b that is the diameter of the cylinder Would be equal to twice of the radius that is 2.2 3.5 cm which is equal to 7 cm Now we see that triangle a b c is a right angle triangle with a c as the hypotenuse of the triangle And a b and b c are the two legs of the triangle And we need to find value of x and from the key idea we know that Ithagoras theorem states in a right angle triangle with hypotenuse c and legs a and b We have c square is equal to a square plus b square So by Pythagoras theorem in triangle a b c Square of the hypotenuse a c that is a c square would be equal to Sum of squares of length of legs that is a b square plus b c square And we know that a c is given by x so we have x square is equal to a b that is 7 So we have 7 square plus b c square that is 17 square So we get x square is equal to 7 square that is 49 plus 17 square that is 289 And we get the value of x square as 338 Now x square is equal to 338 implies that x is equal to square root of 338 Now by taking the positive square root as height cannot be negative We get the value of x as 18.38 centimeters approximately So we get the value of x as 18.38 centimeters So we can say that height of the longest straw 18.38 centimeters approximately Which is the required answer This completes our session. Hope you enjoyed this session