7th Grade Math

658 Measurement and Proportional Reasoning

12. PUZZLES The world’s largest cube puzzle is in Knoxville, Tennessee. It
    measures 6 feet on each side. The scale factor between a standard cube
    puzzle and largest puzzle is _^1
    24
    . Find the surface area and volume of the
    standard cube puzzle.

1313 Two spheres are similar in shape. The scale factor between the smaller

B sphere and the larger sphere is

_^3

4

. If the volume of the smaller sphere is
126.9 cubic meters, what is the volume of the larger sphere?

Determine whether each statement is always, sometimes, or never true.

14. Two prisms with equal bases are similar.


15. Similar solids have equal volumes.


16. Two cubes are similar.


17. A prism and pyramid are similar.


18. Find the missing

10.5 ft 3 ft

7 ft

1.5 f t

y ft

x ft

measure for the

pair of similar solids.

19. Two similar cylinders
    18 cm

6 cm

Cylinder A Cylinder B

S.A. = 5,425.92 cm^2 V = 1,130.4 cm^3

are shown.

a. What is the ratio of

their radii?

b. What is the ratio of their

surface areas? volumes?

c. Find the surface area

of Cylinder B.

d. Find the volume of Cylinder A.

20. GRAPHIC NOVEL Refer to the graphic novel frame below. Use formula r = _dt
    to calculate the speeds. Express in miles per hour.

Now find how

fast the cars

were traveling.

You will need the

distances and

times you

converted in

Lesson 1D.

Real-World Link

Cube Puzzles

The world’s largest

automated cube

puzzle solves itself

every 30 seconds.

The record time

a standard cube

puzzle was solved

in 2008 was

7.08 seconds.

R

C

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