 Hi and welcome to the session. Let us discuss the following question. Question says, a well of diameter 3 meters is dug 14 meters deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 meters. To form our embankment, find the height of the embankment. First of all, let us understand that volume of cylinder is equal to pi r square h, where r is the radius of the cylinder and h is the height of the cylinder. Also, area enclosed between two circles is equal to pi multiplied by r square minus r square, where r is the radius of the outer circle and small r is the radius of the inner circle. Now, we will use these formulas as our key idea to solve the given question. Let us now start with the solution. We have given a well and we know well is in the form of a cylinder. So, volume of a dugout is equal to volume of cylindrical well. Now, earth is spread out evenly all around the well to form an embankment. So, volume of this circular embankment must be equal to volume of earth dugout. Now, first of all, we will find out volume of earth dugout. Now, we are given that diameter of the circular well is equal to 3 meters. This implies radius of the well that is r is equal to 3 upon 2 meters, which is further equal to 1.5 meters. Now, we are given that depth of the well is equal to 14 meters or we can say height of the well that is h is equal to 14 meters. Now, we know volume of the earth dugout is equal to volume of cylindrical well and we know volume of cylinder is equal to pi r square h, where r is the radius of the cylinder and h is the height of the cylinder. Now, substituting corresponding values of pi r and h in this formula, we get 22 upon 7 multiplied by square of 1.5. Multiply it by 14 meter cube. Now, we can cancel common factor 7 from numerator and denominator both and we get 44 multiplied by 2.25 meter cube is equal to volume of earth dugout. Now, we know volume of the earth dugout is equal to volume of this circular embankment. Now, we will find out volume of circular embankment. Now, embankment is 4 meter wide. This is given in the question and volume of embankment is equal to area of embankment multiplied by height of embankment. Let us now find out area of embankment. Clearly, we can see this circle represents the circle of the well and this circle represents the circle of the embankment. So, area of embankment is equal to area of outer circle minus area of inner circle. From key idea, we know area enclosed between the circles is equal to pi multiplied by r square minus r square where r is the radius of the outer circle and this r is the radius of the inner circle. Now, clearly in this figure we can see radius of inner circle is equal to 1.5 meters and radius of outer circle is equal to 1.5 plus 4 meters. We know width of embankment is equal to 4 meters. So, to find radius of outer circle we will add 4 and 1.5. So, we get 5.5 meters is equal to radius of outer circle. Now, we will substitute corresponding values of r and r in this expression. Now, we can write area of embankment is equal to pi multiplied by square of 5.5 minus square of 1.5. Now, we know a square minus b square is equal to a minus b multiplied by a plus b. So, we can write pi multiplied by 5.5 plus 1.5 multiplied by 5.5 minus 1.5. Now, this is further equal to pi multiplied by 7 multiplied by 4. We know 5.5 plus 1.5 is equal to 7 and 5.5 minus 1.5 is equal to 4. Now, we will substitute 22 upon 7 for pi and we get 22 upon 7 multiplied by 7 multiplied by 4 meters square. Now, 7 and 7 will get cancelled and we get 88 meters square is equal to area of embankment. Now, volume of earth on embankment is equal to area of embankment multiplied by height of embankment. Let us assume that height of embankment is h. Now, we know volume of earth dug out from the well is equal to volume of earth on embankment. So, we can write volume of earth dug out is equal to volume of earth on embankment. We know volume of earth dug out is equal to 44 multiplied by 2.25 meter cube. So, we can write 44 multiplied by 2.25 is equal to area of embankment multiplied by height of embankment. We know volume of earth on embankment is equal to area multiplied by height. Now, we have already shown above that area of embankment is equal to 88 meters square. So, we can write 44 multiplied by 2.25 is equal to 88 multiplied by h. Now, dividing both the sides of this expression by 88 we get 44 multiplied by 2.25 upon 88 is equal to h. Now, we will cancel common factor 44 from numerator and denominator both. Now, we get 2.25 upon 2 is equal to height of embankment or we can simply write it as 1.125 meters is equal to height of embankment. So, the required answer is height of embankment is equal to 1.125 meters. This completes the session. Hope you understood the solution. Take care and have a nice day.