VOLUME of Cylinders Essential Question? How do you find the volume of a cylinder? 8.G.9

Common Core Standard: 8.G ─ Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Objectives: To find the volume of a cylinder.

Curriculum Vocabulary Area (área): The number of square units needed to cover a given surface. Base (base, en numeracíon): A side of a polygon; a face of a three-dimensional figure by which the figure is measured or classified. Circumference (circunferencia): The distance around a circle. Diameter (diámetro): A line segment that passes through the center of a circle and has endpoints on the circle, or the length of that segment.

Curriculum Vocabulary Height (altura): In a pyramid or cone, the perpendicular distance from the base to the opposite vertex. In a triangle or quadrilateral, the perpendicular distance from the base to the opposite vertex or side. In a prism or cylinder, the perpendicular distance between the bases.

Curriculum Vocabulary Length (longitud): The distance from one end to the other end of an object. Perimeter (perímetro): The distance around a polygon. Radius (radio): A line segment with one endpoint at the center of the circle and the other endpoint on the circle, or the length of that segment.

Curriculum Vocabulary Right Angle (ángulo recto): An angle that measures 90˚. Volume (volumen): The number of cubic units needed to fill a given space. Width (ancho): The linear extent or measurement of something from side to side, usually being the shortest dimension.

Curriculum Vocabulary Cone (cono): A three-dimensional figure with one vertex and one circular base. Cylinder (cilindro): A three-dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface. Sphere (esfera): A three-dimensional figure with all points the same distance from the center.

Volume of Cylinders A CYLINDER is a three- dimensional figure that has two congruent circular bases that lie in parallel planes. The VOLUME of any three-dimensional figure is the number of cubic units needed to fill the space taken up by the solid figure.

Volume of Cylinders Think of a cylinder. It’s base is a CIRCLE A CYLINDER can be described as a STACK of CIRCLES This is the BASE (B) of the cylinder What is the formula to find the area of a circle? 𝐴 𝑐𝑖𝑟𝑐𝑙𝑒 =𝜋 𝑟 2 Base=𝜋 𝑟 2

Volume of Cylinders 𝑩=𝝅 𝒓 𝟐 h Since any CYLINDER can be described as a STACK of CIRCLES The VOLUME OF THE CYLINDER can be described as The AREA OF EACH CIRCLE (the base B) 𝑩=𝝅 𝒓 𝟐 times the HEIGHT OF THE STACK (h) 𝑩=𝝅 𝒓 𝟐 h

Therefore the formula for the Volume of Cylinders Therefore the formula for the VOLUME OF A CYLINDER is 𝑽 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓 =𝑩𝒉 or 𝑽 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓 =𝝅 𝒓 𝟐 𝒉 𝑩=𝝅 𝒓 𝟐 h

Using the Volume of a Cylinder Formula Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Using the Volume of a Cylinder Formula Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Using the Volume of a Cylinder Formula One of the bass drums used in a marching band has a diameter of 18 inches and a depth of 14 inches. Find the volume of the drum to the nearest tenth . Use 3.14 for π.

Using the Volume of a Cylinder Formula The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank.