 Hello and welcome to the session. In this session, we will discuss a question which says that a pen stand made up of wood is in shape of a cuboid with three equations of the shape of square pyramids. The dimensions of the cuboid are 15 centimetres by 10 centimetres and by 3.5 centimetres the side of each of the square pyramids is 1 centimetre and the depth is 2 centimetres find the volume of the wood in the entire stand. Now before starting the solution of this question, we should know some results. First is volume of the prism is equal to area of its base into height and volume of the pyramid is equal to 1 by 3 into area of its base into height. Now these results will work out as a key idea but solving out the given question. Now let us start with the solution of the given question. Now in this question we are supposed to find the volume of the wood in a pen stand that is we have to find the volume of the wood in this pen stand which is in the shape of a cuboid with three equations of the shape of a square pyramid. Now it is given the dimensions of the cuboid are 15 centimetres by 10 centimetres by 3.5 centimetres. Now for cuboid length n is given as 15 centimetres w is given as 10 centimetres and height h is given as 3.5 centimetres. Depressions are square pyramid also it is given each square pyramid is equal to 2 centimetres. Now to make the depressions the wood is removed from the cuboid. So volume output will be equal to volume of the cuboid into three depressions. Now volume of the cuboid means volume of this rectangular prism. Three depressions means volume of these three pyramids. Now by using the key idea we can find out the volume of prism and the volume of pyramid. Now volume of the cuboid that is volume of this rectangular prism is equal to area of its place now where the base is rectangular in shape so its area will be equal to length into width into the height of this rectangular prism which is now we have l is equal to 15 centimetres but v is equal to 10 centimetres and h is equal to 3.5 centimetres. So volume of the cuboid will be equal to 10 into 3.5 which is equal to 525 centimetre cubed now the volume of one depressions to shape of a square pyramid is equal to 1 by 3 into into height the base of this pyramid is a square with side 1 centimetre so its area will be equal to side into side the depth of this pyramid is given as 2 centimetres which means height is given as 2 centimetres. This is equal to 1 by 3 into area of its place which is a square with side 1 centimetre so the area will be equal to 1 centimetre into 1 centimetre into height which is given as 2 centimetres. Now this is equal to 2 by 3 centimetre cubed. Now the volume of one depression is 2 by 3 centimetre cubed so the volume of two depressions will be equal to 3 into the volume of one depression which is equal to 2 by 3 centimetre cubed now 3 into 1 is 3 so this is equal to 2 centimetre cubed. Now we have got the volume of cuboid as 525 centimetre cubed and volume of 3 depressions is equal to 2 centimetre cubed. Now the volume of wood is equal to volume of cuboid minus volume of 3 depressions which is equal to 525 centimetre cubed minus 2 centimetre cubed which is equal to 23 centimetre cubed so the volume of wood in the entire stand is equal to 523 centimetre cubed and this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.