Surface area & volumeUNIT 4

PrismsSECTION 1

Prism: three dimensional shape with two parallel sides Bases: sides parallel to each other Lateral faces: sides that are not the bases

PRISMS

Volume = length × width × heightExample 1: Find the volume of a prism with a

length of 5 inches, a width of 7 inches, and a height of 2 inches.

Example 2: Find the rectangular width of a prism with a volume of 72, a length of 6, and a height of 3.

RECTANGULAR PRISM

Example 3: Find the height (in terms of x) of a rectangular prism with a volume of 4x2 – 8x – 32, a length of 4, and a width of x – 4.

Example 4: What is the longest lineyou can draw in this rectangularprism?

CHALLENGE YOURSELF!

PyramidsSECTION 2

Lateral Side

Base

Height(Altitude)Lateral Height

(“Slant height”)

One base is a regular polygon (all edges congruent)

Lateral faces are isosceles triangles Lateral area = area of triangles added together

PYRAMID

Pyramid Volume = BhB = AREA of baseh = height

Pyramid lateral area = PlP = Perimeter of base l = Slant height

Ex.: Find the volume and lateral area of a pyramid with a square base with sides of 12 inches and a height of 8 inches.

PYRAMID FORMULAS

13

12

Base

8l = ?

12

CylindersSECTION 3

CYLINDERS

Base

Lateral Area

Volume = Bh B = Area of base (B = πr2) h = height r = radius

Lateral Area = 2πrhExamples:

Find the volume of a cylinder with a radius of 3 and a height of 10. Express your answer in terms of π.

Find the lateral area of the same cylinder. Round your answer to the nearest tenth.

FORMULAS FOR A CYLINDER

ConesSECTION 4

CONES

Base

Lateral Area

Lateral Height(“Slant” Height)

Apex

Volume = Bh B = Area of base (B = πr2) h = height, r = radius

Lateral Area = πrl Where does this formula come

from?

Find the lateral area and surface area of a cone with a diameter of 12 and a height of 8. Express your answer in terms of π.

Find the volume of the same cone to the nearest tenth.

CONE FORMULAS

13

8

SpheresSECTION 4

SPHERES

Diameter

Volume = πr3

Surface Area = 4πr2

Example: Find the volume of a sphere with a surface area of 144π. (Hint: Find the radius first!)

SPHERE FORMULAS

43