Grade 7 MATATAG Volume of Rectangular Pyramid PDF

Grade 7 MATATAG Volume of Rectangular Pyramid  OBJECTIVES explain inductively the volume of a rectangular pyramid, leading to the identification of the formula find the volume of a rectangular pyramid  Lesson Sequence Recap:...

Grade 7 MATATAG Volume of Rectangular Pyramid  OBJECTIVES explain inductively the volume of a rectangular pyramid, leading to the identification of the formula find the volume of a rectangular pyramid  Lesson Sequence Recap: Area of a Rectangle Volume of a Rectangular Prism Lesson: Derivation of Volume of a Rectangular Pyramid Solving Volume of a Rectangular Pyramid  Recap Area of a Rectangle w=4 l=7 A = (7)(4) 28 square units  Recap Volume of a Rectangular Prism https://www.geogebra.org/m/rp9qga8c Deriving Volume of a Pyramid  Pyramid A pyramid is a three- dimensional solid with a polygonal base and triangular faces that converge to a single point called the apex. How is the volume of a rectangular pyramid derived? https://www.geogebra.org/m/gkuka5cj  Rectangular Pyramid A rectangular pyramid is a type of pyramid where the base is a rectangle. It has four triangular faces that meet at the apex, and each triangular face is connected to one side of the rectangular base. How is the volume of a rectangular pyramid derived? Volume of a Rectangular Pyramid  Solving Volume of a Rectangular Pyramid  Solving Volume of a Rectangular Pyramid Example 1. A rectangular pyramid whose base area is 120 𝑓𝑡 and height of 9 𝑓𝑡. Find the 2 volume of the pyramid. Solution: 1 𝑉pyramid = 𝐵ℎ 3 1 𝑉 = (120)(9) ℎ = 9 𝑓𝑡 3 1 𝑉= 3 (1080) 3 The volume of the 𝑉= 360 𝑓𝑡 2 rectangular pyramid 𝐵 = 120 𝑓𝑡 is 360 𝑓𝑡 3  Solving Volume of a Rectangular Pyramid Example 2. Find the volume of a rectangular pyramid if its base length is 10 𝑚𝑒𝑡𝑒𝑟𝑠, its base width is 6 𝑚𝑒𝑡𝑒𝑟𝑠, and its height is 14 𝑚𝑒𝑡𝑒𝑟𝑠. Solution: 1 𝑉pyramid = 𝑙𝑤ℎ 3 1 𝑉 = (10)(6)(14) = 14 𝑚 3 1 𝑉= 3 (840) 3 The volume of the =6𝑚 𝑉= 280 𝑚 rectangular pyramid = 10 𝑚 is 280 𝑚3  Solving Volume of a Rectangular Pyramid Example 3. A rectangular pyramid has a base length of 10 𝑓𝑒𝑒𝑡 and a width of 7 𝑓𝑒𝑒𝑡. The height is approximately 9.5 𝑓𝑒𝑒𝑡. Estimate the volume of the pyramid. Solution: 1 𝑉pyramid = 𝑙𝑤ℎ 3 ℎ = 9.5 𝑓𝑡 1 𝑉 = (10)(7)(9.5) 3 1 𝑉= 3 (665) 3 𝑤 = 7 𝑓𝑡 𝑉= 221.67 𝑓𝑡 The volume of the rectangular pyramid 𝑙 = 10 𝑓𝑡 is 221.67 𝑓𝑡 3  Solving Volume of a Rectangular Pyramid Example 4 The volume of a rectangular pyramid is 300 𝑚 , 3 and the base area is 50 𝑚. Find the height of the pyramid. 2 50 50 Given: 300 = ℎ 300 = 3 ℎ 3 3 50 V = 300 𝑚 300 = 16.67ℎ 300(3) = (3)ℎ 2 300 3 B = 50 𝑚 =ℎ 16.67 900 = 50ℎ Solution: 17.9964 … = ℎ 900 1 = ℎ 𝑉pyramid = 𝐵ℎ ≈ 18 50 3 1 ℎ = 18 𝑚 ℎ = 18 𝑚 300 = (50)ℎ 3 The height of the rectangular pyramid is 18 m  Activity Find the volume of the solid figure with the following measurements: 1. A rectangular pyramid has a base area of 150 𝑓𝑡 2 and a height of 12 𝑓𝑡. Find the volume of the pyramid. 2.Find the volume of a rectangular pyramid if its base length is 8 𝑚𝑒𝑡𝑒𝑟𝑠, its base width is 5 𝑚𝑒𝑡𝑒𝑟𝑠, and its height is 16 𝑚𝑒𝑡𝑒𝑟𝑠. 3. A rectangular pyramid has a base length of 9 feet and a width of 6 feet. The height is approximately 10.5 feet. Estimate the volume of the pyramid. 4.The volume of a rectangular pyramid is 450 𝑚 , and the base area 3 is 75 𝑚2. Find the height of the pyramid.  Activity SOLUTIONS: 1. A rectangular pyramid has a base area of 150 𝑓𝑡 2 and a height of 12 𝑓𝑡. Find the volume of the pyramid. The volume of the pyramid is 600 cubic feet.  Activity SOLUTIONS: 2. Find the volume of a rectangular pyramid if its base length is 8 𝑚𝑒𝑡𝑒𝑟𝑠, its base width is 5 𝑚𝑒𝑡𝑒𝑟𝑠, and its height is 16 𝑚𝑒𝑡𝑒𝑟𝑠. Rounding to the second decimal place, the volume of the pyramid is 213.33 cubic meters.  Activity SOLUTIONS: 3. A rectangular pyramid has a base length of 9 feet and a width of 6 feet. The height is approximately 10.5 feet. Estimate the volume of the pyramid. The estimated volume of the pyramid is 189 cubic feet.  Activity SOLUTIONS: 4. The volume of a rectangular pyramid is 450 𝑚 , and the base area is 3 75 𝑚2. Find the height of the pyramid. 1350 = ℎ 75 75 18 = ℎ 450 = 3 ℎ ℎ = 18 𝑚 75 450(3) = 3 (3)ℎ The height of the 1350 = 75ℎ pyramid is 18 meters.  Up Next Volume of a Rectangular Pyramid Solving Problems Thank You for Listening