1 Geometry Regents Lomac Date 3/23 due 3/24 3D: Cross Sections and Rotating 2D 9.5R
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1 1 Geometry Regents Lomac Date 3/23 due 3/24 3D: Cross Sections and Rotating 2D Name Per LO: I can solve problems involving volumes of General Cones and General Cylinders and can determine shapes formed by rotating 2D shapes. DO NOW On the back of this packet (1) Cross Sections of general cones Can you make a connection between general cones and dilations? Explain your thoughts. (2) Cross Sections of general cylinders and general cones Parallel cross sections of general cylinders are Parallel cross sections of general cones are
2 2 (3) Cross Sections of... he diagram below shows cross sections of a figure starting at the bottom of the figure with the diagram on the far left and moving toward the top on the far right. Describe at least one description of what the three dimensional figure looks like. (here are multiple answers that are valid.) (4) Rotating 2D shapes to make 3D shapes Use the cutout shapes to help you answer the questions from here on. Rotating around a point VS. Rotating around a segment Rotate WO around point W. Rotate RE around R (you choose the number of degrees) (rotate a full 360 ) Sketch the resulting figure. Sketch the resulting figure. W O R E Describe the difference between the two figures you sketched. Rotating around a point produces a figure while rotating around a segment or line produces a figure.
3 3 (5) If AN = 8, N = 6, and A = 10 and triangle AN is rotated about segment AN, what shape will be formed? Sketch the shape, label the measurments, and find the volume of the figure. A N (6) Sketch the figure formed when sector DUG is rotated about segment UG. Describe the figure and find its volume if the radius of sector DUG is 8. Leave your answer in terms of π. D U G (7) Sketch the figure formed when rectangle BLOX is rotated about segment LX. Describe the figure and find its volume if BX = 2(BL) and the perimeter of BLOX is 192. B L X O
4 4 (8) riangle AN is rotated about segment A, what shape will be formed? Sketch and describe the shape. A N (9) Sketch the figure formed when rectangle BLOX is rotated about line m, which is the perpendicular bisector of BL. Describe the figure and find its volume if BX is 87.3 cm and BL = 42.5 cm. Round to the nearest hundredth. m B L X O (10) Sketch the figure formed when triangle AN is rotated about line q which passes through point A. q AN. Describe the figure and find its volume if AN = 28 and N = 11. Round to the nearest integer. A q N
5 (6) Exit icket ON HE LAS PAGE 5 (7) Homework Provide sufficient evidence for each response. (1) (2) When each shape below is rotated about the bold line, a 3D shape is formed. Name the shape for each figure.
6 6 (7) internet Homework (3) (a) (b) (4) Find the measure of x in each diagram below. A G H C 2 B E x D F 5 J x I
7 Exit icket Name Date Per 7 he LO (Learning Outcomes) are written below your name on the front of this packet. Demonstrate your achievement of these outcomes by doing the following: (1) he diagram below shows cross sections of a figure starting at the bottom of the figure with the diagram on the far left and moving toward the top on the far right. Write at least one possible description of what the three dimensional figure looks like. (here are multiple answers that are valid.) (2) What shape is formed when the triangle below is rotated about line m? m
8 8 DO NOW Name Date Per (1) Cakes sold by Destiny s Deserts are made in the shape of cones or cylinders. he cones are 6 in diameter and 6 tall while the cylinders are 4 in diameter and 6 tall. Should Destiny charge the same amount for both cakes, charge more for the cone cakes, or more for the cylinder cakes? Justify your answer based on the amount of ingredients she will need for each cake. Start by sketching the two cake shapes and labeling them with their measurements. (Use the reference page on the back of 9.0 to help you.) (2) What about the cartoon is supposed to make people smile? How does the girl s slicing technique relate to Cavalieri s Principle?
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Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Methods in Mathematics (Linked Pair Pilot) Unit 2 Geometry and Algebra Monday 11 November 2013
Class : VI - Mathematics
O. P. JINDAL SCHOOL, RAIGARH (CG) 496 001 Phone : 07762-227042, 227293, (Extn. 227001-49801, 02, 04, 06); Fax : 07762-262613; e-mail: opjsraigarh@jspl.com; website : www.opjsrgh.in Class : VI - Mathematics
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Geometry: Unit 11 Test Review Find the area of each of the following figures. If part of the figure is shaded, find the area of the shaded part. ssume O is the center of the circle. If it is not possible
h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.
ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this