mostly molly grade 6 learners fourth quarter this time our topic relationship of volume of prisms and pyramids and other 3d figures after going through this lesson you are expected to determine the relationship of the volume between a rectangular prism and a pyramid a cylinder and a cone and a cylinder and spear hi pupils i know you're very excited because it is the first lesson of the fourth quarter in this lesson you will be able to know the relationship between the volumes of a prism to a pyramid to start this lesson look at the figures below how many cubic units are there in one layer how many layers fill the figure in the figures it has 24 cubic units in one layer and it has 8 layers if you are going to count the total number of cubic units in the figure it has 190 cubic units which represent the volume of this figure if you can still remember that volume of a rectangular prism is the product of its length width and height according to the book 21st century mathletes 2016 volume of a prism is the amount of space inside it and it is measured in cubic units which means it tells you how many cubes of a given size it takes to fill the prism what if we are to get the volume of a pyramid where in the dimensions of the base and its height is the same as the given rectangular prism will you be able to determine the number of cubic units inside the pyramid let us take a look at this figure let us fill the rectangular prism with water using the pyramid the figure shows that if you fill the rectangular prism with water using a pyramid push base and the height is the same as the given rectangular prism it takes three pyramid to fill in a rectangular prism therefore the volume of the given prism is 192 cubic units then the volume of the pyramid is 192 divided by 3 equals 64 cubic units vice versa if the volume of the given pyramid is 64 cubic units therefore volume of the rectangular prism is 64 times 3 equals 192 what if we have to pour water in a cylinder using a coil of the same base and height it takes three cones to fill in the cylinder the cone and the cylinder have the same base and height example find the volume of the cone inside the ceiling there the cone and ceiling there have the same base and height the volume of cylinder is 288 cubic units to find the volume of cone volume equals 288 divided by 3 and that is 96 cubic units and that is the volume of cone another example find the volume of the ceiling there cone and ceiling there have the same base and high volume of cone is 78 cubic units the volume of ceiling there is three times the volume of cone therefore to get the volume of the cylinder in the example volume equals 78 cubic units times 3 equals 234 cubic units what if we have to pour water in the ceiling there using a sphere of the same base and height the volume of ice sphere is two thirds of the volume of a cylinder the cylinder and spear have the same base and height example find the volume of the spear inside the cylinder the spear and the ceiling there have the same base and height if the volume of a ceiling there is ported to cubic units let's find out the volume of spear so volume equals two thirds times 42 two times 42 equals 84 divided by 3 equals volume equals 28 cubic units and that is the volume of a sphere another example find the volume of the cylinder the sphere and cylinder have the same base and height the volume of spear is 51 cubic units the volume of a sphere is two thirds of the volume of a cylinder therefore to get the volume of the cylinder in the example volume equals 51 times three halves and that is 153 cubic units divided by two so volume equals 76.5 cubic units and that is the volume of the cylinder therefore from the given examples we say that if the prism and pyramid have the same base and height it takes three pyramids to fill in the volume of the prism or we could say that the volume of pyramid is one third the volume of the prism with the same base and height learning task 1 find the volume of the second picture using the volume of the first given the given solid figures have the same base and height number one the volume above ceiling there is 78 cubic centimeters find the volume of the hole since the cone is one third the volume of a cylinder therefore 78 cubic centimeters divided by three so the volume of cone is 26 cubic centimeters number two the volume of the pyramid is 36 cubic centimeters find the volume of the prism since the volume of the pyramid is 1 3 of the volume of the prism therefore volume equals 36 cubic centimeters times three so the volume of a preset is 108 cubic centimeters number three the volume of the ceiling there is 198 cubic meters find the volume of the given sphere the volume of a spear is two-thirds of the volume of a cylinder therefore volume equals 188 cubic meters times two turns 198 times 2 equals 396 divided by 3 therefore the volume of my spear is 132 cubic meters can you answer number four and number five learning task two using cardboard or a folder create a rectangular prism and pyramid given that their dimensions are the same using the solid figures proved that it takes three pyramids to fill in a prism with the same base and height then complete the statement below number one volume of the pyramid equals blank times volume of rectangular prism number two for rectangular prism volume equals length times width times long number three so for pyramid volume equals length times width time side gang this is the rubric so now you will be graded in this learning pass submit the solid figures during the retrieval of answer sheet learning to task three read its question carefully then write the letter of the correct answer number one what is the relationship of the volume between a prism and a pyramid of the same dimensions a the volume of the pyramid is two-thirds of the volume of the prism b the volume of the pyramid is three-thirds of the volume of the prison c the volume of the pyramid is one-third of the volume of the prism the the volume of the pyramid is three halves of the volume of the prism number two the volume of a cone is blank the volume of a cylinder if both of the same dimensions a double ball beat rice c twice d four times number three how many cones can fill the holy sphere with the same dimension a1 b2 c3 b4 if the volume of a ceiling there is 120 cubic meters what will be the volume of a cone with the same dimension a 180 cubic meters b 60 cubic meters c 40 cubic meters d 30 cubic meters number five what is the length of the edge of a cube if it has a volume of 27 cubic inches pain and injest b6 inches c 3 inches d two inches [Music] please share this to your classmates um you