+0  
 
+1
511
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avatar+1442 

1:   A right square pyramid with base edges of length 8sqrt2 units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

 

 

2:   A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 3-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?

 

3:   A circle with center O has radius 8 units and circle P has radius 2 units. The circles are externally tangent to each other at point Q. Segment TS is the common external tangent to circle O and circle P at points T and S, respectively. What is the length of segment OS? Express your answer in simplest radical form.

 

4:   In the diagram, if triangle ABC and triangle PQR are equilateral, then what is the measure of angle CXY in degrees?

 

5:   Circle \(\Gamma\) is the incircle of triangle ABC and is also the circumcircle of triangle XYZ. The point X is on line BC, point Y is on overline AB, and the point Z is on line AC. If angle A=40 degrees, angle B=60 degrees, and angle C=80 degrees, what is the measure of angle AYX?

 

 

The answer is not 130, I've seen a similar problem with this answer but I have tried it and it is not that.

     

                                                                                                 | | |

 

I know this is a lot of problems but I would appreciate the answers to any of them individually if that helps.  Thanks so much!

 May 14, 2018
 #1
avatar+10066 
+1

1:   A right square pyramid with base edges of length 8sqrt2 units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

https://picload.org/view/doorrdli/96.jpg.html

laugh

 

2:   A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 3-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?

https://picload.org/view/doordrgl/97.jpg.html

laugh

 May 14, 2018
edited by Omi67  May 14, 2018
 #2
avatar+10066 
+1

 

3:   A circle with center O has radius 8 units and circle P has radius 2 units. The circles are externally tangent to each other at point Q. Segment TS is the common external tangent to circle O and circle P at points T and S, respectively. What is the length of segment OS? Express your answer in simplest radical form.

https://picload.org/view/doorppir/98.jpg.html

 

laugh

 

4:   In the diagram, if triangle ABC and triangle PQR are equilateral, then what is the measure of angle CXY in degrees?

https://picload.org/view/doorpwcl/99.jpg.html

 

laugh

5:   Circle  is the incircle of triangle ABC and is also the circumcircle of triangle XYZ. The point X is on line BC, point Y is on overline AB, and the point Z is on line AC. If angle A=40 degrees, angle B=60 degrees, and angle C=80 degrees, what is the measure of angle AYX?


https://picload.org/view/doorwaol/100.jpg.html

 

wink

 May 15, 2018
edited by Omi67  May 15, 2018
edited by Omi67  May 15, 2018
 #3
avatar+1442 
+2

Thank you SO much for all the answers Omi!  These were so helpful!

 May 15, 2018

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