Geometry Test Study Guide
Volume:
a. Prisms- Formula: V=bwh or V=Bh
Important Reminders:
- B does not mean base; it means area of the base.
- For a rectangular prism, you can use V=bwh, but for a triangular prism you
must use V=Bh.
- In a triangular prism, the triangle face is always the base.
- To find B in a triangular prism, use the area of a triangle formula: A= ½bh
b. Cylinders- Formula: V=πr 2h or V=Bh
Important Reminders:
- Don’t forget to square the base!
c. Pyramids- Formula: V= ⅓Bh
Important Reminders:
- B does not mean base; it means area of the base.
- To find B in a triangular pyramid, use the area of a triangle formula: A= ½bh
d. Cones- Formula: V=⅓ πr 2h or V= ⅓Bh
Important Reminders:
- Don’t forget to square the base!
e. Composite figures: Find the volume of each figure and then add both volumes at the
end.
Sample Problems (Answers will be on the last page):
Find the volume of the following figures:
1.
4.
2.
3.
5.
6. The triangular faces of a triangular prism have a height of 5 m and a base of 8 m. The height of the
prism is 10 m. The triangular prism is connected to a cylinder. The height of the cylinder is 4 m and the
radius is 6 m. Find the volume of the composite figure to the nearest tenth. Use 3.14 for π.
Surface Area
a. Prisms- Formula: S.A.=Ph+2B
Important Reminders:
- P means Perimeter of the Base. This means you need to add up all of the sides
of the base of your figure.
- B does not mean base; it means area of the base.
- In a triangular prism, the triangle face is always the base.
- To find B in a triangular prism, use the area of a triangle formula: A= ½bh
b. Cylinders- Formula: S.A.=2 πrh+ 2πr 2
Important Reminders:
- If the diameter is given, you must divide it by 2 to find the radius.
c. Pyramids- Formula: S.A.=½Pl+B
Important Reminders:
- P means Perimeter of the Base. This means you need to add up all of the sides
of the base of your figure.
- B does not mean base; it means area of the base.
- To find B in a triangular pyramid, use the area of a triangle formula: A= ½bh
- l means slant height
d. Cones- Formula: S.A.=½(2πr)l+B
Important Reminders:
- If the diameter is given, you must divide it by 2 to find the radius.
- l means slant height
- B does not mean base; it means area of the base.
- Use the formula for area of a circle to find B
e. Composite figures: Find the surface are for each figure, add them up, then subtract the
area of the surface that is connecting both figures; multiplied by 2.
Sample Problems (Answers will be on the last page):
Find the surface area of the following figures:
7.
8.
10.
11.
9.
12.
Changing Dimensions
Dimensions
Perimeter
Area
Surface Area
Volume
x2
x2
x22
x22
x23
x3
x3
x32
x32
x33
x½
x½
x(½)2
x(½)2
x(½)3
Remember that the big number each column has in common is the scale factor.
Sample Problems (Answers will be on the last page):
13. If you buy a new rug that has double the dimensions of the old rug in your room, how will the area
of your new rug compare to the area of your old rug?
14. The surface area of a box is 35 in2. What is the surface area of a similar box that is larger by a scale
factor of 7?
15. The bath tub in Ravina’s house measures 46 in. by 36 in. by 24 in. Another bath tub with a similar
shape is smaller by a scale factor of ½. There are 231 in3 in 1 gallon. Estimate how many more gallons
the larger bath tub holds.
16. The scale factor of the larger of two similar rectangular prisms is 3. The volume of the smaller prism
is 12 cm3. What is the volume of the larger rectangular prism?
Translations, Reflections and Rotations
-
Be able to identify these types of translations.
Be able to predict the location of a figure after these transformations on a graph and by
using the coordinates.
Translation: Slide
Reflection: Flip
Rotation: Turn
When dealing with coordinates of reflections, remember that based on whichever axis you’re
reflecting on, those coordinates will stay the same and the other will be the opposite.
- If you are reflecting across the y-axis, the y-coordinates will stay the same and the x-coordinates
will be the opposite.
- If you are reflecting across the x-axis, the x-coordinates will stay the same and the y-coordinates
will be the opposite.
Sample Problems (Answers will be on the last page):
Identify the type of transformation for numbers 17-18.
17.
18.
19. Graph a reflection across the yaxis.
Dilations
-
To dilate a figure, multiply all of the coordinates of the vertices by the scale factor.
Dilated figures are the same shape, but a different size, therefore they are similar.
Sample Problems (Answers will be on the last page):
20. Draw the vertices of the image of ∆ABC after a dilation by a scale factor of 2. What are the vertices
of the image?
Remember that for this test, you will be given a Reference Sheet. You DO NOT need to memorize the
formulas for Volume and Surface Area; you just need to know how to use them.
Sample Problems Answers
V= 329.7 m3
V= 384 yd3
V= 3,250 ft3
V= 74.7 ft3
V= 150 yd3
3
6. V= 652.2 m
7. S.A.= 606 in2
8. S.A= 538.8 ft2
9. S.A.=261 m2
10. S.A.= 170.28 m2
11. S.A.= 122.46 cm2
12. S.A.= 66 ft2
13. The area of the new rug will be 4 times greater than the area of the old rug.
14. 1,715 in2
15. 150 gallons more
16. 324 cm3
17. Translation
18. Reflection
1.
2.
3.
4.
5.
19.
20.
Vertices: (0,0); (2,4); (6,2)