practice: orthographic & foundation drawings name...
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Practice: Orthographic & Foundation Drawings Name: ___________________________ Geometry 1-2 Date: ________________ Period: _____ A foundation drawing (or map plan) shows the base of a structure (its top view) and the height of each part. Match each foundation drawing with its three-dimensional object. Assume there are no hidden cubes.
A B C D E F G H 3 1 2 1 2 3 1 1 2 3 2 1 2 1 3 1 3 1 1 1 3 2 1 1 1 1 1 1
1. 2. 3. 4.
5. 6. 7. 8. Look at #8 again. Assuming the object consists of 7 cubes, sketch its foundation drawing. An orthographic drawing shows the top view, front view, and right-side view of a three-dimensional object.
Example:
The illustrations show a figure and its orthographic drawings. Label the side view, front view, and top view.
15.
21.
18.
24.
Match the figure (J, K, L, M) with its corresponding side view, front view, and top view (3, 4, 8, 9).
Practice: 3-D drawings on TAKS 25. The Transamerica Pyramid is a building located in San Francisco, California, that resembles a square pyramid. The diagram below shows a front and side view of the building. If the back view of the building is similar to the front view and the side views are similar to each other, which of the following best represents the top view? A B C D 26. The drawing shows the top view of a structure built with cubes as well as the number of cubes in each column of the structure.
Which 3-dimensional view represents the same structure?
27. The front, side, and top views of a solid build with cubes are shown below.
How many cubes are needed to construct this solid?
28. How many cubes would you use to make the structure on the right? Draw a top view of the structure, and include the number of cubes in each part.
32. The diagram below shows the top view of a structure built with identical cubes, as well as the number of cubes in each column of the structure.
30. Which of the following best represents the front view of the solid shown
29. What is the volume of a 3-dimensional object with the dimensions shown in the 3 views below?
31. The 3-dimensional figure shown below represents a structure that Corina built with 9 cubes.
Which of the following best represents the top view of Corina's 9-cube structure?
Which 3-dimensional view best represents the same structure?
11-2, 11-3 Surface Areas of Prisms, Cylinders, Pyramids, and Cones Name: ___________________________ Class Exercises Date: ________________ Period: _____ Use the following steps to find the lateral area (LA), base area (B), and surface area (SA) of 3-D figures:
1. Write the name of the 3D figure. 2. Shade in one base, to remind yourself to find the perimeter and area of the BASE (not the lateral faces). 3. Write the formula. 4. Substitute the variables with values. 5. Solve. 6. Write the answer with correct units.
1. Name of 3D figure: ______________________________
LA = __________ = ________________________________________ = _______________ formula substitute with values and solve answer with units B = __________ = ________________________________________ = _______________ formula substitute with values and solve answer with units SA = __________ = ________________________________________ = _______________ formula substitute with values and solve answer with units
2. Name of 3D figure: ______________________________
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
3. Name of 3D figure: ______________________________
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
4. Name of 3D figure: _____Regular Square Pyramid_____
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
5. Name of 3D figure: ______________________________
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
6. Name of 3D figure: ______________________________
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
11-2, 11-3 Surface Areas of Prisms, Cylinders, Pyramids, and Cones
7. Name of 3D figure: ____Regular Triangular Pyramid____
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
8. Name of 3D figure: _____Oblique Cylinder___________
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
9. Name of 3D figure: ____Regular Pentagonal Prism____
LA = __________ = ________________________________________ = _______________
B = __________ = ________________________________________ = _______________
SA = __________ = ________________________________________ = _______________
10. Describe the effects on the surface area of a right cone if every dimension of the cone is divided by 5. You do
not need to calculate the SA (surface area) itself. Simply state the ratio of the new SA to the old SA.
11. Find the surface area (exterior surface only, including bottom).
12. Find the surface area (exterior surface only, including bottom).
13. Find the surface area (exterior surface only, including bottom).
11-4, 11-5 Volumes of Prisms, Cylinders, Pyramids, and Cones Name: ___________________________ Class Exercises Date: ________________ Period: _____ Use the following steps to find the volume (V) of 3-D figures:
1. Write the name of the 3D figure. 2. Shade in one base, to remind yourself to find the area of the BASE (not the lateral faces). 3. Write the formula. Remember that the formula for the Base depends on the SHAPE of the base! 4. Substitute the variables with values. 5. Solve. Give exact answers (in simplest radical form or in terms of π). 6. Write the answer with correct units.
1. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________ formula substitute with values and solve answer with units
V = __________ = ________________________________________ = _______________ formula substitute with values and solve answer with units
2. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
3. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
4. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
5. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
6. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
7. Name of 3D figure: ______________________________
B = __________ = ________________________________________ = _______________
V = __________ = ________________________________________ = _______________
8. Name of 3D figure: _______________ and _______________
B = __________ = _______________ V = __________ = _________________________
B = __________ = _______________ V = __________ = _________________________
Composite volume = _________________________
Mixed Surface area and Volume 9. Find the Surface Area and Volume of the trapezoidal prism below: 10. Stephanie has 2 different types of cake pans, round and rectangular. All of her pans are two inches in height. Which will hold more cake batter? One 9 in. by 13 in. rectangular pan or two 9 in diameter round pans
or
11. A hot tub was built in the shape of a regular hexagonal prism with a 4 foot edge. How many cubic feet of water will the hot tub hold if it is filled to one foot from the top.
6 ft
4 ft
12. A cylinder with a 90° slice removed is part of a kit used to make a wooden castle model. How many cubic inches of wood is needed to make four cylinders shown below.
13. You are making candles of the indicated shape by melting a block of wax that is 8 cm by 9 cm by 10 cm. How many candles of each given shape can be molded?
4 cm 4 cm 6 in
7 cm 6 cm 12 in
top view of castle
90°
14. An ice-cream shop sells sugar cones and waffle cones. If the outside of each cone is dipped in chocolate, which cone will require more chocolate? A sugar cone with diameter of 2 inches and height of 4 inches or a waffle cone with radius of 1.5 inches and height of 3 inches.
15. How many dice with a 2 cm edge can be placed completely inside a box that is 4 cm long, 2 cm wide and 6 cm tall?
16. The pencils shown below are hexagonal prisms. They each have a height of 17 cm without the eraser. The base edge of the pencil has a length of 0.3 cm. How many square centimeters of each hexagonal pencil is painted?
17. Each one of the plastic tubes shown below has a diameter of 0.6 cm and is 18.5 cm long. If they are open on both ends, how many square centimeters of plastic are needed to make twenty tubes?
18. A cone and a cylinder have the same radius and the same height. If the cone is used to pour water into the cylinder, predict how many times will it take to fill the cylinder completely?
19. A pyramid and a prism have the same base area and the same height. The pyramid displaces 2 liters of water when it is submerged. How many liters of water would be displaced if the rectangular prism was submerged?
20. The total surface area of the cylinder is approximately 88 cm2. The lateral surface area is
about 63 cm2. Find the approximate area of one base.
Answers: 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
Inside Outside Circle - Effects of changing dimensions on perimeter, circumference, area, surface area and volume 1) If the radius of a can of soda is doubled and the height remains the same, how much more soda will the larger can hold than the smaller can?
2) If the length and width of a rectangular gift box is halved and the height remains the same, by what factor does the volume of the box decrease?
3) The length of a rectangle is multiplied by 5. By what factor does the area of the rectangle increase?
4) The base and height of a right triangle are divided by 3. By what factor does the area of the triangle decrease?
5) If the radius were doubled, what effect would it have on the circumference of a circle?
6) If the diameter and the height both double, what effect will it have on the total volume of a cone?
7) The length, width, and height of a cube are changes to 5 times their original size. By what factor does the surface area of the cube increase?
8) If the height of a rectangular gift box is tripled and the other dimensions remain the same, by what factor does the volume of the box increase?
9) John purchased a new cylindrical pole to hold his basketball goal. Its height remained the same as the old pole but its diameter is twice as long. How much more paint will he need to paint only the lateral surface area of the new pole than he needed for the old pole?
10) If the length, width, and height of a rectangular gift box were doubled, by what factor does the volume of the box increase? By what factor does the surface area of the box increase?
11) The volume of one cube is 8 cubic in. The volume of another cube is 64 cu in. Find the ratio of the surface area of the smaller cube to the surface area of the larger cube.
12) If the diameter of a personal size pizza is tripled, how much more pizza will the larger one contain than the smaller personal size pizza?
Dimensional Change Name: ___________________________ HHS Geometry, Ms. Leung Date: ________________ Period: _____
This jar has 200 cubic inches of honey. I have a bigger jar whose height and diameter are twice as long as my first jar. That means the bigger jar has twice as much honey, yum!
Both of you are estimating too little honey. I think the bigger jar will have 8 times as much honey, because 23 is equal to 8.
You’re right that it will have more honey, but I think that it will have four times as much honey, since the height is being multiplied by 2, and the diameter is being multiplied by 2, and 2 times 2 is four.
Who do you agree with the most – Winnie, Tigger, or Piglet? Explain why.
Surface Area and Volume Word Problems Name _______________________________ Date ____________________ Period _____ Show all work. For each problem, sketch and label the dimensions of the object if no diagram is given. State each formula that you use. Then rewrite the formula with values and solve.
4. If you cut a 1-inch square out of each corner of an 8.5-by-11-inch piece of paper and fold it into a box without a lid, what is the volume of the container?
3. If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two longer sides together, you get a tall, thin cylinder. If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two shorter sides together, you get a short, fat cylinder. Which of the two cylinders has the greater volume? Justify your answers by showing calculations. Which of the two cylinders has greater surface area, provided you also cover to bases with paper? Justify your answers by showing calculations. How do the lateral areas of the two cylinders compare? Justify your answer.
5. Claudette and Marie are planning to paint the exterior walls of their country farmhouse (all vertical surfaces) and to put new cedar shingles on the roof. The paint they like best costs $25 per gallon and covers 250 square feet per gallon. The wood shingles cost $65 per bundle, and each bundle covers 100 square feet. How much will this home improvement cost? All measurements are in feet.
6. You have a cylinder with a radius of 3 inches. You fill it with water to a height of 4 inches. You pour all the water into another cylinder, which has a radius of 5 inches. How high will the water reach in the other cylinder, assuming the other cylinder was empty before pouring in the water? You pour all the water into a square prism. Each side of the square base has a length of 4 inches. How high will the water reach in the square prism?
7. The Khafre pyramid in Egypt has a square base that is 214.5 meters on each side and a vertical height of 143.5 meters. Calculate the slant height of the pyramid. Round to the nearest hundredth. Calculate the lateral area of the pyramid. Calculate the volume of the pyramid.
Surface Area and Volume Word Problems Name _______________________________ Date ____________________ Period _____
8. The cylinder’s height and diameter are equal to the diameter of the ball. What is the volume of the cylinder inside the cylinder but outside the ball?
15. Using a ruler, measure the dimensions of the following net. Calculate the volume of the rectangular prism.
16. What is the volume of the 3-D figure shown?
Example for Regular Square Pyramid (base is a square and faces are congruent isosceles triangles) Use Pythagorean Theorem to find unknown parts. Example: If EF = 18 and AD = 16, find EC, BD, ED and the perimeter of the base.
E
Answers: 3. shorter sides together; shorter sides together; same. 4. 58.5 in3. 5. $1570. 6. 36/25 in; 9/4 π in. 7. 179.15 m; 76,855 m2; 2,200,834 m3. 8. 18π u3. 15. 5.4 cm3. 16. 480 ft3. 52. G. Example: EC = 2√89, BD = 8√2, ED = 2√97, perimeter = 32√2 units.
G D
C
B A
F
Lateral edge (ED=EB=EA=EG)
Altitude
Slant height
Side of base