02.26.2019 Agenda Bell Ringer Bell Ringer Volume Video: https://www.youtube.com/wat ch?v=aPXvrFMyhSU Cornell notes Topic: Volume E.Q. How can I calculate the volume of a given shape? KWL Chart

Volume & Surface Area Section 6.2

Volume The volume is a measure of the space inside a solid object. Volume is measure of 3 dimensions. The units of volume are cube length or length3. Example of volume units are cm3, cubic feet, cubic meters or inches3.

Surface Area Surface area is the flat area on the surface of a three- dimensional object. What you do is compute the area of all the sides of an object and then add them up.

The Cube For an arbitrary cube with edges that have length L, H, and W. The volume is V = LWH. The surface area of the cube is the sum of the areas of each face. SA = 2LW + 2HW + 2LH. H W L

Length Width Height How would you work out the volume?

The Sphere The volume of a sphere with radius r, is V = (4/3)πr3. The surface area is SA = 4πr2.

The cylinder The volume of the cylinder is height of the cylinder times the area of a circle. V = πr2h. The surface area of a cylinder has two parts. The ends are circles so each circle has an area of πr2. The lateral surface can be thought of as a rectangle wound into a circle. One side of the rectangle is h, the other side is the circumference of the circle which is 2πr. 2πr h h

Volume of a Cylinder A cylinder is a special type of prism with a circular cross-section. Volume = area of circular base × height h r Recall that the area of a circle is equal to πr2.

The pyramid and cone The pyramid and cone have similar formulas for their volume. The basic volume formula is V = (1/3)Ah. Where A is the area of the base. For a pyramid, the area of the base A is just the area of a rectangle. For a cone, the area of the base is the area of a circle. pyramid cone

Prisms A prism is a 3-D shape that has a constant cross-section along its length. has the same hexagonal cross-section throughout its length. For example, this hexagonal prism This is called a hexagonal prism because its cross-section is a hexagon. Tell pupils that cubes and cuboids are also examples of prisms. Prisms are usually named after the shape of their cross-section.

Volume of a prism The volume of a prism is found by multiplying the area of its cross-section by its length or height. A h A l

What is the volume of this triangular prism? Volume of a prism What is the volume of this triangular prism? 7.2 cm 4 cm 5 cm Area of cross-section = ½ × 5 × 4 = 10 cm2 Volume of prism = 10 × 7.2 = 72 cm3

Reference https://www.asu.edu/courses/mat142ej/.../volume_an d_surface_area_dalesandro.ppt