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

2. 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.

3. Objectives:
To find the volume of a cylinder.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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

11. 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

12. 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

13. 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.

14. 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.

15. 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.

16. 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.