CIRCLES ON TAKS NAME CLASS PD DUE
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1 CIRCLES ON TAKS NAME CLASS PD DUE 1. On the calculator: Let s say the radius is 2. Find the area. Now let s double the radius to 4 and find the area. How do these two numbers relate?
2 2. The formula for circumference is : We want to solve for such that the rest is on the other side of the equation. 3. Volume of a cylinder is We have the volume We have the diameter Radius All that is missing is the height. Find it. 4. What would you need to find out how much air is needed to fill a basketball? A. Surface area B. What the basketball is made of C. Circumference D. Volume
3 5. A circle has degrees. So, the sum of the interior angles must add up to degrees. There are 8 pieces if pie. So each angle Therefore Angle B= These make ISOSCELES triangles so the angles A and C must be The sum of the interior angles of a triangle adds up to degrees. therefore angle A= 6. Follow the same process as in #5.
4 7. draw a picture of a rectangular prism and a cylinder! 8. Write out the units of the volume and time Volume = BH Volume = How fast does the water come out? rate this is a How long to empty it? looking at the units what do you need to do to get an answer of just time? 9. Careful!! This is like one of the rectangle ones we studied. Make sure to draw out the tiles with their dimensions!! Hummmmm! Do we want to work this in inches or feet?? Notice both dimensions are used What is the area of the counter top in inches? A = LW L = 5ft 4 = inches W =2 ft 2 in = inches A = How big is the sink? A = πr 2 A = Counter sink = - = (area to be tiled) Each tile is 2in by 2 inches. How big is each tile?. How many will he need to cover the counter?
5 10. Lateral surface area does not include the ends. It is just the area of the cylinder without the ends. If you cut a cylinder down the side, you will see that the width is the circumference. Circumference * height = area 11. You should be able to find the area of the rectangle and the area of the circle, subtract them. Now you have to deal with the hole in the middle. Add it? Subtract it? Show work. 12. A cylinder has a base where the radius is height is. What is the volume? The
6 13. Think, What is the radius? Only one answer has in it. 14. Find the height: Formula V = Double that height. Find volume. Compare the volumes
7 15. This is a ratio problem. So we will set up a proportion and cross multiply. Find the Circumference. Formula How many degrees in a circle? Degrees : Circumference Whole circle : _ Wedge of circle : _ 16. The proper way to find this diameter is to use the distance formula inset above. Let point A be point 1 and point b be point 2. Find the distance. Remember the RADIUS would be ½ of this. Show work: Now logic. Pretend A and B are dropped down to the X axis. What is the distance from -2 to 10? Based on THIS circle, would that be close to the diameter? What answer does that lead you to?
8 17. Is this a circle problem or a triangle problem? With what you know about circles, how long is it from the center of the circle to F? You finish. 18. Draw a radius on the circle. A. Make a point M and a point N and connect them. (Straight line) Remember, you can move M and N around. B. Could MN be longer than R? C. Could MN be the same length as r? D. What is 2r? Can MN be the same as 2r E. Can MN be longer than 2r?
9 19. Remember Archimedes principle? Volume displaces volume. This is not hard if you take it step by step. Step 1. Find the volume of water in the cylinder. Formula? Does the 18 mean anything? Step 2. While the volume of the sphere is given, What is the formula for volume of a sphere What is the volume? Step 3. Remember Archimedes, just add the two. + = Step 4. Using new volume and the original base, find the new height.
10 Remember what domain and range are.
11 22. Looks hard, but you have the tools: Volume of a sphere. Formula? Find the volume of the balloon. What was its diameter? Multiply that by 1.5 Find the volume of the expanded balloon. Divide new volume by original volume and CAREFULLY make a decision. 23. SHOW YOUR WORK:
12 Other Polygons Poly (many) gon (sides) Triangles Three sided figures Quadrilaterals 4 sides Five sided figures Six sided figures Heptagons Seven sided figures 8 sided figures 9 sides Decagons -10sides
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