Supporting Standard Describe the volume formula V = Bh of a cylinder in terms of its base area and its height. Supporting Standard Describe THE VOLUME FORMULA V = Bh OF A CYLINDER IN TERMS OF ITS BASE AREA AND ITS HEIGHT Including, but not limited to: Three-dimensional figure a figure that has measurements including length, width (depth), and height – Attributes of cylinders Cylinder 2 congruent, parallel circular bases 1 curved surface Bases of a cylinder the two congruent, opposite circular bases – Height of a cylinder the length of a line segment that is perpendicular to both bases – Pi (π) the ratio of the circumference to the diameter of a circle – Approximations for pi π 3.14 ≈ π ≈ Volume the measurement attribute of the amount of space occupied by matter – One way to measure volume is a three-dimensional cubic measure Formulas for volume from STAAR Grade 8 Mathematics Reference Materials Cylinder V = Bh, where B represents the base area and h represents the height of the cylinder which is the number of times the base area is repeated or layered The base of a cylinder is a circle whose area may be found with the formula, A = πr2, meaning the base area, B, may be found with the formula B = πr2; therefore, the volume of a cylinder may be found using V = Bh or V = πr2h. Ex: Relationship between volume of a prism and volume of a cylinder The formula used to determine volume of a prism is = and the formula to determine the volume of a cylinder is = V Bh, V Bh. The base area depends on the shape of the base. (e.g., the shape of the base of a triangular prism is a triangle; the shape of the base of a cylinder is a circle, etc.) Ex: Relationship between volume of a cylinder, its base area, and height
Supporting Standard Describe the volume formula V = Bh of a cylinder in terms of its base area and its height. Supporting Standard Describe THE VOLUME FORMULA V = Bh OF A CYLINDER IN TERMS OF ITS BASE AREA AND ITS HEIGHT Including, but not limited to: Three-dimensional figure – a figure that has measurements including length, width (depth), and height Attributes of cylinders Cylinder 2 congruent, parallel circular bases 1 curved surface Bases of a cylinder – the two congruent, opposite circular bases Height of a cylinder – the length of a line segment that is perpendicular to both bases Pi (π) – the ratio of the circumference to the diameter of a circle Approximations for pi π ≈ 3.14 π ≈ Volume – the measurement attribute of the amount of space occupied by matter One way to measure volume is a three-dimensional cubic measure Formulas for volume from STAAR Grade 8 Mathematics Reference Materials Cylinder V = Bh, where B represents the base area and h represents the height of the cylinder which is the number of times the base area is repeated or layered The base of a cylinder is a circle whose area may be found with the formula, A = πr2, meaning the base area, B, may be found with the formula B = πr2; therefore, the volume of a cylinder may be found using V = Bh or V = πr2h. Ex: Relationship between volume of a prism and volume of a cylinder The formula used to determine volume of a prism is V = Bh, and the formula to determine the volume of a cylinder is V = Bh. The base area depends on the shape of the base. (e.g., the shape of the base of a triangular prism is a triangle; the shape of the base of a cylinder is a circle, etc.) Ex: Relationship between volume of a cylinder, its base area, and height