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Math 10/11GeometryWe looked at exponents last week: let’s see if you remember:How does COVID produce exponential growth? What is an exponent and how is it different than times?What is another place you find exponents?Geometry is often done by tradespeople and it involves measuring things in the real world.It goes from simple to complicated, but even complicated isn’t that bad.It involves putting a number (usually a measurement) into formula and then punching the rest into a calculator.The main geometric Formulas are:Perimeter Distance around somethingWood for a banisterAreaSize of a flat surfaceTiles for the floorSurface AreaSurface of a 3D objectCardboard for a boxVolume (Capacity)Interior of a 3D objectConcrete for a blockIn this diagram, surface area would look like volume.People often learn formulas for temperature and mass (weight) at the same time.Examples: Perimeter of a rectangle = side + side + side + side Let’s say you needed strings of lights for the edge of your house. The house is 6 meters, by 8 meters: 6 + 8 + 6 + 8 = 28 meters of lights.Volume of a cube: s3 (All the sides are the same length in a cube).You need to buy concrete to make a large concrete block for you barbeque. The block should be 3 Feet by 3 Feet by 3 Feet.33 = 3 x 3 x 3 = 27 cubic Feet (cubic feet are confusingly written ft3). Area of a rectangle is length x width or lwIf you needed to make a table cloth for a table that was 2 metres x 1 metre.You would need 2 x 1 or 3 square metres (and maybe some extra) or 3m2Surface area is confusing: It’s still the same as area, because the exterior of something is flat. However, surface area is used for 3D objects so you have to figure out all of the sides of that object and add them together.So you decide to buy a lot of wrapping paper and wrap a washing machine for your mom. The box is 3ft x 3 ft x 4 ft. You need to buy wrapping paper for 6 sides of the box (boxes usually have 6 sides like a dice). Side A 3 x 4, Side B 3 x 3, Side C 3 x 4, Side D 3 x 4, Side E 3 x 4, Side F 3 x 3. OR: Side A 12, Side B 9, Side C 12, Side D: 12, Side E 12, Side F 9. 12 + 9 + 12 + 12 + 12 + 9 = 66 square meters.(Notice you had to multiply to find each side and add to put them together). (Also it’s in square meters, m2, not cubic meters, m3).Other ShapesIf you want to measure round, triangular or other shapes you need different formulas, but I have put them on my website.Questions (Do at least 4 of the following questions)These start easy and get harder. Perimeter, Area, Surface Area and Volume. Chapter 3What is the perimeter of a rectangle that is 4m by 6m?How much sand could fit inside our gym if it is 100 feet x 110 feet and 40 feet high?If you are going to cover a hanging Christmas decoration in gold leaf (paint) how much is needed for a cube of 6cm per side?If you have a new aquarium in your office that is 45” high by 79” long by 30” deep. If it doesn’t have a lid, how much glass (in square inches) is needed to build it.A party planner is designing a conical (Cone-like) tent. The tent has no floor and a radius of 3’, a height of 4’ and a slant height of 5ft. How much canvas is needed for this tent?A roll of vinyl flooring costs 30.00/ square metre. How much would it cost to cover a floor that is exactly 5m by 8m.Tony needs to put salt on the parking area for his pet store. His whole lot is 74’ by 120’, but the building covers 25’ by 5’ of that lot. If one bag of salt covers 10 square feet, how many bags will he need?What is the surface area of a circle that has a radius of 5 feet? What is its surface area in square meters?If there is a huge cylindrical water tank that is 15m tall and has a radius of 4m. What is the capacity in litres? (1m3, = 1000 l).Draw a net of the following shape: a pyramid with a square base of 250 feet, a height of 120 feet. Also calculate its volume. ................
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