Pre-AP Geometry Worksheet 7.7 Pre-AP Geometry Name: ___________________ Worksheet 7.7 Date: _______ Period: ____ Solve. Show all work including the ratios used. 1. A city stores rock salt in a hemispherical shaped building that is 82 feet in diameter. The building holds 3,366 tons of salt. The city planners decide to build another smaller building of the same shape. The dimensions of the new building will be three-fourths those of the original building. Find the storage capacity of the new hemisphere to the nearest ton. 2. Two similar cones have radii of 4 cm and 6 cm. The total area of the smaller cone is 36π cm 2 . Find the total area of the larger cone. 3. A cube of lead weighs 40 lb. How much does a cube of lead weigh if each dimension is one-half as large? 4. The lateral areas of two similar solids are 16π cm 2 and 9π cm 2 . The volume of the larger solid is 128π cm 3 . Find the volume of the smaller solid.
Transcript
Pre-AP Geometry Worksheet 7.7
Pre-AP Geometry Name: ___________________ Worksheet 7.7 Date: _______ Period: ____ Solve. Show all work including the ratios used. 1. A city stores rock salt in a hemispherical shaped building that is 82 feet in diameter. The building
holds 3,366 tons of salt. The city planners decide to build another smaller building of the same shape. The dimensions of the new building will be three-fourths those of the original building. Find the storage capacity of the new hemisphere to the nearest ton.
2. Two similar cones have radii of 4 cm and 6 cm. The total area of the smaller cone is 36π cm2. Find the total area of the larger cone. 3. A cube of lead weighs 40 lb. How much does a cube of lead weigh if each dimension is one-half as large? 4. The lateral areas of two similar solids are 16π cm2 and 9π cm2. The volume of the larger solid is
128π cm3. Find the volume of the smaller solid.
Pre-AP Geometry Worksheet 7.7
5. A block of ice weighs 2 lb. How much does a similarly shaped block of ice weigh if each dimension is twice as large?
6. How much does a statue of George Washington weigh if a similarly shaped scale model of the
statue, in which each dimension is one-twelfth as large as the original, weighs 3 lb.? 7. A cone-shaped pile of sand weighs 250 lb. How much does a similarly shaped pile of sand weigh?
if each dimension is six times as large?
8. The radius of the larger sphere shown below was multiplied by a factor of 12
to produce the smaller
sphere. How does the total surface area of the smaller sphere compare to the total surface area of the larger sphere?
A. The total surface area of the smaller sphere is 12
as large.
B. The total surface area of the smaller sphere is π1 as large.
C. The total surface area of the smaller sphere is 14
as large.
D. The total surface area of the smaller sphere is 18
as large.
Radius = r1
Radius = r2
Pre-AP Geometry Worksheet 7.7
9. A block of wood weighs 24 pounds. How much does a similarly shaped block weigh if each dimension is one-fourth as large?
10. Mr. Kelly’s company manufactures a cylindrical soup can with a volume of 226 cubic inches. If the
diameter stays the same and the height is doubled, what will happen to the can’s volume? a) It will remain the same. b) It will double. c) It will triple. d) It will quadruple. 11. The total areas of two similar pyramids are 225 m2 and 441 m2. The volume of the larger pyramid is
1029 m3. Find the volume of the smaller pyramid. 12. If the ratio of the volumes of two prisms is 1331:729 and the lateral area of the smaller prism is 324 m2, find the lateral area of the larger prism. 13. Loretta designed a three-dimensional scale model of a department store. The volume of the scale
model was 35 cubic feet and the ratio of the dimensions of the model to the dimensions of the store is 1:20. What was the volume of the actual department store that Loretta planned to build?
Pre-AP Geometry Worksheet 7.7
20 cm10 cm
14. The radius and height of the smaller cylinder below were multiplied by a factor of 4.
How does the volume of the larger cylinder compare to the volume of the smaller cylinder?
A. The volume of the larger cylinder is 4 times as large. B. The volume of the larger cylinder is 4π times as large. C. The volume of the larger cylinder is 16 times as large. D. The volume of the larger cylinder is 64 times as large.
15. Nathaniel had a cup in the shape of a cone with a height of 20 centimeters. He filled the cup to the top with 16 fluid ounces of water and then drank some. If the remaining water in the cup was 10 centimeters high, how much water did he drink?
A) 2 ounces B) 8 ounces C) 12 ounces D) 14 ounces KEY TO ODDS: 1) 1420 tons 3) 5 pounds 5) 16 pounds 7) 54,000 pounds
For Exercises 4–6, are the two figures similar? If so, give the scale factor of the first figure to the second figure.
4. 5.
6. a cylinder and a square prism both with 3-in. radius and 1-in. height
Each pair of figures is similar. Use the given information to find the scale factor of the smaller figure to the larger figure.
7. 8.
The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
9. S.A. = 248 in.2, V = ? 10. S.A. = 52 ft2 , V = ?
S.A. = 558 in.2, V = 810 in.3 S.A. = 208 ft2, V = 192 ft3
The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.
11. V = 27 in.3, S.A. = 63 in.2 12. V = 2 yd3, S.A. = 13 yd2
V = 125 in.3, S.A. = ? V = 250 yd3, S.A. = ?
13. Apply Mathematics (1)(A) There are 750 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
14. Refer to the figure in Problem 6. How would the surface area and volume of the cylinder have been affected if the height were multiplied by 2 and the radius were multiplied by 3? Explain your reasoning.
15. Explain Mathematical ideas (1)(G) Are all spheres similar? Explain.
16. Connect Mathematical Ideas (1)(F) Is there a value of x for which the rectangular prisms at the right are similar? Explain.
17. The volume of a spherical balloon with radius 3.1 cm is about 125 cm3. Estimate the volume of a similar balloon with radius 6.2 cm.
9 cm 12 cm
27 cm18 cm
18 m
30 m20 m
12 m
V ! 250p ft3 V ! 432p ft3
V ! 216 in.3 V ! 343 in.3
STEM
80 m40 m
45 m 30 m
60 mx m
602 Lesson 14-7 Surface Areas and Volumes of Related Solids
18. Justify Mathematical Arguments (1)(G) A carpenter is making a blanket chest based on an antique chest. Both chests have the shape of a rectangular prism. The length, width, and height of the new chest will all be 4 in. greater than the respective dimensions of the antique. Will the chests be similar? Explain.
19. Analyze Mathematical Relationships (1)(F) Some stories say that Paul Bunyan was ten times as tall as the average human. Assume that Paul Bunyan’s bone structure was proportional to that of ordinary people.
a. Strength of bones is proportional to the area of their cross section. How many times as strong as the average person’s bones would Paul Bunyan’s bones be?
b. Weights of objects made of like material are proportional to their volumes. How many times the average person’s weight would Paul Bunyan’s weight be?
c. Human leg bones can support about 6 times the average person’s weight. Use your answers to parts (a) and (b) to explain why Paul Bunyan could not exist with a bone structure that was proportional to that of ordinary people.
20. Square pyramids A and B are similar. In pyramid A, each base edge is 12 cm. In pyramid B, each base edge is 3 cm and the volume is 6 cm3.
a. Find the volume of pyramid A.
b. Find the ratio of the surface area of A to the surface area of B.
c. Find the surface area of each pyramid.
TEXAS Test Practice
21. The slant heights of two similar pyramids are in the ratio 1 : 5. The volume of the smaller pyramid is 60 m3. What is the volume in cubic meters of the larger pyramid?
22. What is the value of x in the figure at the right?
23. A dilation maps △JEN onto △J′E′N′. If JE = 4.5 ft, EN = 6 ft, and J′E′ = 13.5 ft, what is E′N′ in feet?
24. △CAR ≅ △BUS, m∠C = 25, and m∠R = 39. What is m∠U ?
25. A regular pentagon has a radius of 5 in. What is the area of the pentagon to the nearest square inch?
