Volume of pyramids and cones

Learning Objectives Recall and correctly apply the formulas for the volume of a pyramid and a cone. Calculate the volume of a right pyramid given its base dimensions and perpendicular height. By the end of of this lesson, students will be able to calculate the volume of a right cone given its radius and perpendicular height. Differentiate between perpendicular height and slant height and identify which is used for volume calculations. Use the Pythagorean theorem to find the perpendicular height when given the slant height and a base dimension (like radius). Solve for a missing dimension (height, radius, or base length) when the volume is provided. Explain the relationship between the volume of a pyramid/cone and a prism/cylinder with the same base and height. Ever wondered...

TermDefinitionExample PyramidA three-dimensional solid with a polygon base and triangular faces that meet at a single point called the apex.The Great Pyramid of Giza has a square base and four triangular faces. ConeA three-dimensional solid with a circular base and a single curved surface that tapers to a point called the apex.An ice cream cone or a standard traffic cone. ApexThe highest point or vertex of a pyramid or cone, opposite the base.The sharp tip of a cone. Base Area (B)The area of the polygon or circle that forms the bottom of the pyramid or cone. The formula for B depends on the shape of the base.For a square pyramid with a side length of 5 cm, the Base Area (B) is 5 cm * 5 cm = 25 cm². Perpendicular Height (h)The straight-line distance from the apex to the center of the base,...

Volume of a Pyramid V = \frac{1}{3} B h Use this formula to find the volume (V) of any pyramid. 'B' represents the area of the pyramid's base (e.g., for a square base, B = side²), and 'h' is the perpendicular height from the apex to the base. Volume of a Cone V = \frac{1}{3} \pi r^2 h Use this formula to find the volume (V) of a cone. 'r' is the radius of the circular base, and 'h' is the perpendicular height. Note that \pi r^2 is the formula for the area of the circular base (B). The 1/3 Relationship Volume_{Pyramid/Cone} = \frac{1}{3} Volume_{Prism/Cylinder} The volume of a pyramid or cone is exactly one-third the volume of a prism or cylinder that has the same base area and the same perpendicular height. This is why the...