Geometry 12.3 Part 1 Cylinders

Right Cylinders

Oblique Cylinders

Today you will learn how to find three measurements about right cylinders. You will find: Right Cylinders Lateral area: L.A. Total area: T.A. Volume: V

Right Cylinder Vocabulary base each is a circle base h r altitude joins the centers of the bases, with length h radius radius of the base is also the radius of the cylinder, r

To find lateral area (L.A.): Multiply circumference by height circumference height Take a can of soup Peel off the label

Lateral Area of a Cylinder: L.A. The lateral area of a cylinder equals the circumference of a base times the height of the cylinder. L.A = 2πrH LA = 12π 8 = 96π square units L.A = dπH L.A = CH which is 6 8

To find total area (T.A.):Take the label (LA) Pop the top and find the area of the base TopBottom Add 2 base areas to the LA A = πr²

Total Area of a Cylinder: T.A. The total area of a cylinder is the lateral area plus twice the area of a base. T.A = L.A. + 2B TA = 96π + 2(π 6²) = 96π + 2(36π) = 96π + 72π = 168π square units 6 8 T.A. = 2πrH + 2πr² which is

To find volume (V):Start with the area of the base Multiply it by height H r That’s how much soup is in the can ! A = πr²

Volume of a Cylinder: V The volume of a cylinder equals the area of a base times the height of the cylinder. V = πr²H V = (π 6²) 8 = 36π 8 = 288π cubic units 6 8

Exercises Find the (a) lateral area (b) total area and (c) volume. 1. (a) LA = CH LA = 4π (3) LA = 12π un² (b) TA = LA + 2B TA = 12π + 2(4π) TA = 20π un² Base area = π 2² = 4π radius: 2 Height: 3 TA = 12π + 8π (c) V = πr²H V = 4π 3 = 12π un³ Base circumference = 2(2)π = 4π

Exercises Find the (a) height (b) lateral area and (c) volume. 2. (b) TA = LA + 2B 24π = LA + 2(4π) LA = 16π un² (a) LA = CH 16π = 4π H H = 4 un Base area = π 2² = 4π (c) V = πr²H V = 4π 4 = 16π un³ Base circumference = 2(2)π = 4π 2. radius: 2 Total Area: 24  24π = LA + 8π

It’s been soup-er having you in class today………… Let’s check out the soup addendum powerpoint.

Homework (1) Finish Notes Exercises #3-5 on a separate sheet (2) Get a Campbell’s soup can and measure it in cm. Find the: (a) LA (b) TA (c) V