 Hi and welcome to the session. I am Deepika here. Let's discuss a question. Is small terrace at a football ground comprises of 15 steps each or which is 50 meter long and built of solid concrete? Each step has a rise of 1 by 4 meter and it dread of 1 by 2 meter. See figure? Calculate the total volume of concrete required to build the terrace. Hint. Volume of concrete required to build the first step is equal to 1 by 4 into 1 by 2 into 50 meter cube. Let's start the solution. We know that the sum of first items of an AP as soon as equal to n by 2 into a plus l where a is first term of an AP and l is last term. Also volume of a cuboid is equal to l into b into h. So this is the key idea behind this question. We will take the help of this key idea to solve the above question. So let's start the solution. Now it is given in the question. Total number of steps is 15. Length of each step is equal to 1 by 2 meter. You can... this length is 50 meter. Now width of each step is equal to 1 by 2 meter. Rise height or rise of... rise of is 1 by 4 meter and dread. This is 1 by 2 meter. So first step... rise of the first step is 1 by 4 meter. Now each step has a rise of 1 by 4 meter. So height of second step is 2 into 1 by 4 meter. Height of third step is 3 into 1 by 4 meter and so on till 15. Height of 15th step is 15 into 1 by 4 meter. Height or rise of second step is equal to 1 by 4 meter and rise of third step and so on. The height and rise of 15 steps is equal to 15 into 1 by 4 meter. Therefore height rise of 15th step is equal to 15 into 1 by 4 meter. V1, V2, V3, so on. V15 be the volumes of the concrete to build up and so on. 15th... V1 according to key idea because step is in cuboidal shape. So L into V into H. L is our 50 into V is our 1 by 2 meter into height. This is 1 by 4. So this is V1 is 50 meter into 1 by 2 meter into 1 by 4 meter. That is V1 is equal to this cube and similarly V2 is equal to length and into breadth V15 is equal to V into 1 by 2 into 15 into 1 by 4 meter cube 4. Total volume of concrete required is V1 plus volume of concrete required to build the first step plus volume of concrete required to build the second step plus volume of concrete required to build the 15th step. So this is equal to or V1 is equal to 50 into 1 by 2 into 1 by 4 plus 50 into 1 by 2 into V2 is 2 into 1 by 4 plus so on V15 is 50 into 1 by 2 into 15 into 1 by 4 meter cube is equal to 50 into 1 by 2 is common in every term to take it as a common factor 15 into 1 by 2. So here we have 1 by 4 plus 2 by 4 plus so on 15 by 4 meter cube 25 by into 1 plus 2 plus 3 plus so on plus 15 meter cube. This is equal to 25 by 4 now use the formula from the key idea that is sum of first 15 terms this is equal to as soon as equal to n by 2 2 that is 15 by 2 into a 1 plus the last term 15. So this is equal to 25 by 4 into 15 by 2 into 16. So on cancellation we get 2 to the 4 this is equal to 25 into 30 meter cube which is equal to 750 meter cube. So 750 meter cube is the total volume of concrete required to build the terrace. Hence the answer for the above question is 750 meter cube. I hope the question is clear to you. Bye and have a nice day.