Volume Surface Area Section 6 2 Volume The

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 length 3. • Example of volume units are cm 3, cubic feet, cubic meters or inches 3.

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 = 2 LW + 2 HW + 2 LH. H W L

The Sphere • The volume of a sphere with radius r, is V = (4/3)πr 3. • The surface area is SA = 4πr 2.

The cylinder • The volume of the cylinder is height of the cylinder times the area of a circle. V = πr 2 h. • The surface area of a cylinder has two parts. The ends are circles so each circle has an area of πr 2. 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 h h

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