Volume of Pyramids and Cones

Master pyramid & cone volumes! Worksheets explain relationships with prisms & cylinders.

Act 1: Rectangular Pyramid vs Rectangular Prism Watch the quick clip. What do you notice? List several things you notice. Record your answer What do you wonder? List several things that you wonder after watching this clip. Record your answer I wonder how many rectangular pyramids it takes to fill this rectangular prism. What is your best guess? Record your answer. Act 2: Giving More Information Watch the clip Do you still feel confident? Want to guess again? Record your answer. Act 3: Experience the Answer Watch the clip. After watching the final act, what can you conclude about the relationship between the volume of a rectangular pyramid and a rectangular prism with the same height and base? Record your answer. Do you think this relationship is true with any shaped pyramid and prism with the same height and base? Explain Record your answer. Triangular Pyramid and Triangular Prism Check out this triangular pyramid and triangular prism. Both have the same height and base. Explain the relationship between the volume of a pyramid and prism with the same base and height. Recorder your answer. Above are the formulas for prisms and pyramids. How does the formula tie into your understanding of the relationship between the volume of a pyramid and prism with the same height and base? Recorder your answer. Still questioning it? Try it yourself! Grab the shapes and try it with rice! Check for Understanding Which statement below is true? The volume of the pyramid is three times the volume of the prism. The volume of the prism is three times the volume of the pyramid. The volume of the prism is one-third the volume of the pyramid. A triangular pyramid has a volume of 150 cubic centimeters. Which of the following represents the volume of a triangular prism with the same area of the base and height? 75 cubic centimeters 300 cubic centimeters 50 cubic centimeters 450 cubic centimeters A triangular prism and a triangular pyramid have congruent heights and bases. Which of the following is true about their relationship and formulas? The pyramid is three times the size of the prism because the volume of the prism is represented as V=(3)(B)(h). The pyramid is one-third the size of the prism because the volume of the prism is represented as . The prism is three times the size of the pyramid because the volume of the pyramid is represented as . The prism is one-third the size of the pyramid because the volume of the prism is represented asV=Bh. Dean has two candles. The volume of his triangular prism candle is 120 cm3. He has another candle in the shape of a triangular pyramid and it has the same base and height as the first candle. What is the volume of the pyramid candle? 40 cubic centimeters 80 cubic centimeters 240 cubic centimeters 60 cubic centimeters Let's Check Out Cones and Cylinders! Do you think there is a relationship between the volume of cones and cylinders? Explain Record your answer. Act 1: What's the question? Watch the clip What do you notice and wonder? How many cones do you think it takes to fill a cylinder with the same base and height? Record your answer. Act 2: Giving More Information What the clip. Any changes in your thoughts? Record your answer. Task 3: Experience the Answer Explain the relationship between volume of a cone and a cylinder with the same base and height. Above are the formulas for the volume of a cylinder and a cone. How do the formulas relate to your explanation? Check for Understanding The cylinder and cone below both have a height of 10cm and a diameter of 10cm.Which description below accurately represents the relationship of the cylinder and cone? ? The volume of the cone is greater than the volume of the cylinder. The volume of the cone is 3 times the volume of the cylinder. The volume of the cylinder is 3 times the volume of the cone. The volume of the cylinder is the volume of the cone. Fill in the blanks below. If a cone and a cylinder have the same diameter and the same height, what is the ratio of the volume of the cone to the volume of the cylinder? Cone: Cylinder 1:3 At a wedding, there was a potato bar. Guests could pick from a cylindrical bowl or a bowl shaped like a cone. Both have the same height and the diameter of their bases are the same.Sara picked the cone shaped bowl and Michael picked the cylindrical bowl. Which description accurately compares their relationship when comparing the volume?? Sara's bowl will hold twice as much as Michael's bowl. Sara's bowl will hold 3 times as much as Michael's bowl. Sara's bowl will hold as much as Michael's bowl. Sara's bowl will hold as much as Michael's bowl. The diagram below shows a cone and a cylinder that have congruent bases and congruent heights.Which statement, where h represents the height of the cone and the height of the cylinder, is true? The volume of the cone and the volume of the cylinder are equivalent. The volume of the cone is 3 times the volume of the cylinder. The volume of the cylinder is 3 times the volume of the cone.