3D Geometry Questions and Answers

TT VE 0 5 y 0 5 0 866 The angle 60 is shown in the unit circle Draw in another angle that has the same sin value 0 5 0 60 0 5 0 5 X

What is the volume of the pyramid below 112 116 4

In physics lab Ellie attaches a wireless sensor to one of the spokes of a bicycle w spinning freely on its axle The graph below shows the sensor s height above the ground in centimeters over time t measured in seconds 50 2 75 48 11 75 48 4 P Sensor s height in cm 20 20 20 7 25 38 16 25 38 01 10 11 12 13 14 15 16 1S Time in seconds

REASONING In Exercises 29 34 tell whether it is possible for a cross section of a cube to have the given shape If it is describe or sketch how the plane could intersect the cube 29 circle 31 rhombus 30 pentagon 32 isosceles triangle 33 hexagon 34 scalene triangle

Find the area of the kite 6 m B D 42 3 Round answer to nearest thousandths

Question A frustum of a pyramid is a part of the pyramid with two parallel bases The lateral faces of the frustum are trapezoids Use the area formula for a trapezold to derive a formula for the lateral area of a frustum of a regular square pyramid with base edge lengths by and by and slant height 2 B 261 63 201 02

Determine the volume of each of the composite solids below 9 11 4 cm 6 cm 13 cm 5 cm 5 6 cm 6 cm 2 cm 4 in 4 in 6 in 5 in

Find the missing length given the volumes for each figure 1 OC 7 mi 791 68 mi 3 492 81 cm 5 7 184 31 km 6 m 65 97 m

18 3 An antihistamine shows sharp peaks at Raman shifts of A 488 725 875 925 and 1350 cm At what wavelengths in nanometers would the Stokes and anti Stokes lines for the antihistamine appear if the source were a a helium neon laser 632 8 nm b an argon ion laser 488 0 nm

4 In a regular 25 gon a What is the measure of each interior angle b What is the measure of each exterior angle

In circle V mYX 106 Solve for x if m YW X 8x 38 If necessary round your answer to the nearest tenth Y W X 4

14 Regular Quadrilateral 15 Regular Octagon 16 Regul

13 Match the correct answer Given WXYZ is a parallelogram XZL WY Prove WXYZ is a rhombus Statements 1 WXYZ is a parallelogram 2 XZLWY 3 2WPX and 4 LWPX and Reasons 1 Given 2 Given XPY are 90 s 3 Def of lines XPY are rt Zb 4 e 5 AWPX and AYPX are rt As 5 Def of rt As XP XP 0 e 7 XZ bisects WY 7 Diags of a bisect each other 8 Def of bisector WP PY 9 9 LL 10 WXXY 10 CPCTC 11 11 with one pair of consecutive sides thom AWPXAYPX b AWPX AYPZ c Reflexove Property of d Transitive Property of

In 15 16 Draw a picture then solve using the appropriate trigonometric function Round sides to the nearest tenth and angles to the nearest degree Don t forget units 15 Linda is flying a kite She has let out 45 yds of string and anchors it to the ground She determines that the angle of elevation of the kite is 58 What is the height of the kite from the ground

The cylinder has a diameter of 12 cm The entire composite figure has a height of 23 cm 12 cm 23 cm B 23 cm What is the volume of this composite figure A 756 cm C 12 cm 8287 cm 900 cm

HW Complete problems 1 7 for independent practice 1 Calculate the following 4 2 Calculate the following 7 3 When you are finished check the solutions with your teacher 3 There are 9 students entering the school district s science project with all students having an equal chance of winning There are medals for 1st 2nd and 3rd place In how many different ways can the medals be awarded to students 4 There are 7 unique names in a bowl In how many orders can 2 names be chosen Hint The word orders implies that each unique order of two names is counted as a possibility OX

4 There are 15 Jolly Ranchers in a jar containing 3 blue 3 red 3 green 3 yellow and 3 purple 3 Jolly Ranchers are chosen at random from the jar What is the probability that all 3 chosen Jolly Ranchers are blue Leave your answer as a simplified fraction Hint Follow the 3 step model in Your Turn 3 Step 1 is set up for you Step 1 How many ways can you choose 3 lolly Ranchers in a jar containing 15 Jolly Ranchers This is n S n S 15C3 Step 2 Step 3

HW Complete problems 1 6 below f 1 Find the surface area of the sphere below 2 ft 4 ft When you are finished check the solutions in the back of the 3 Find the surface area of the sphere below 12 8 km 5 Find the surface area of the sphere below Give your answer in terms of 2 Find the surface area of the sphere below 3 1 m 4 Find the surface area of the sphere below 23 4 mi 6 Find the surface area of the sphere below Give your answer in terms of 6 m tional Complete problems 2 3 7 9 10 12 13 15 from your textbook on separate lined paper for extra actice When you are finished check the odd problems for solutiona

3 Find the volume of the square pyramid below Lesson 18 2 1 2 point 9 7 ft 10 ft or 7 ft 4 Find the volume of the cone below Lesson 18 3 1 2 point 10 ft A 8 ft 9 ft 5 Find the volume of the composite figure below Leave your answer in t notation for this problem Lesson 18 3 2 points 3 16 ft Find the volume of the sphere below Lesson 18 4 1 point 10 ft Find the volume of a hemisphere that has a diameter of 26 inches Lesson 18 4 1 point

Lesson 19 2 Checkpoint Checkpoint below Once you have completed the above problems and checked your solutions complete the Lesson Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 You want to reuse an old cookie tin can into a new decorative tin by spray painting the surface Find the surface area of the following cylinder below Use 3 14 for Round to the nearest tenth 6 in Dunich Butter Condi 10 in 2 If one 11 oz spray paint can provide coverage for up to 864 square inches will you have enough for two coats Explain your reasoning

N Your Turn 2 Find the surface area of each composite figure Use 3 14 for m Round Hint Scomposite prism surface area cylinder lateral area 3 cm 9 cm 9 in 2 cm 5 in 5 cm 4 cm 3 in 3 in 5 in 7 in 3 7 mm 0 3 mm 6 mm

Your Turn Find the volume of each composite figure 1 16 m 16 m 10 m 4m 5m 2 8 ft 8 ft 8 ft

the volume he cylinder to the right has radius of 2 cm and height of 10 cm Give our answer in terms of it

The gift box is a right prism Find the total amount of paper needed to wrap the box Do not count overlap 1 18 in 5 in 5 in

Find the volume of the composite figure Round to the nearest tenth 1 30 cm 15 cm 12 cm

2 Find the volume of each figure 1 1 cm 4 cm 3 cm 5 cm 2 cm 4 cm

Read the question and type your response in the box provided On circle C shown below the measure of ZBCA is 104 C B Enter the measure of ZBDA in degrees

X Y 2 y 3 2 x 1 1 3 33