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12.8 similar solid CW

Total questions: 22

Worksheet time: 55mins

Name
Class
Date
1.
What does similar mean?
a)
same shape and same size
b)
same size
c)
sames shape
d)
neither
2.

Determine whether each pair of solids is similar, congruent or neither. If the solids are similar, state the scale factor( use column :)

(a)  

3.

Determine whether each pair of solids is similar, congruent or neither. If the solids are similar, state the scale factor

(a)  

4.

Two similar pyramids have slant heights of 6 inches and 12 inches. What is the ratio of the surface area of the small pyramid to the surface area of the large pyramid?( use column :)

(a)  

5.

Two spheres have surface areas of 100 π\pi  square centimeters and 16 π\pi square centimeters. what is the ratio of the volume of the large sphere to the volume of the small sphere?( use column :)



(a)  

6.

Two rectangular prism are similar. The height of the first prism is 6 yards and the height of the other prism is 9 feet. If the volume of the first prism is 810 cubic yards, what is the volume of the other prism?( Type numerical part only)

(a)  

7.

Two suitcases are similar rectangular prisms. The smaller suitcase is 68 centimeters long,47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long.

a. What is the scale factor of the prisms?( use column :)

(a)  

8.

Two suitcases are similar rectangular prisms. The smaller suitcase is 68 centimeters long,47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long.

B. what is the volume of the larger suitcase? round to the nearest tenth.( Type numerical part only)

(a)  

9.

What is the volume of the larger solid shown ?( round to nearest hundreds, type numerical only)

(a)  

10.

What is the surface area of the smaller solid shown below?(Type as improper fraction, numerical only)

(a)  

11.

22. Two cylinders are similar. The height of the first cylinder is 23cm and the height of the other cylinder is 8 in. If the volume of the first cylinder is 552 π cm3\pi\ cm^3  , what is the volume of the other prism? Use 2.54cm=1in.

(a)  

12.

Two similar cones have volumes of 343 π\pi   cubic centimeter and 512 π\pi  cubic centimeters. The height of each cone is equal to 3 times it radius. Find the radius and height of both cones.

(a)  

13.

Two tents are in the shape of hemispheres, with circular floors. The ratio of their floor area is 9:12.25. If the diameter of the smaller tent is 6 teet, what is the volume of the larger tent? round to the nearest tenth.

(a)  

14.

Plane P is parallel to the base of the cone C, and the volume of the cone above the plane is 18\frac{1}{8}   of the volume of cone C. Find the height of cone C.

(a)  

15.

Writing in Math: Explain why all spheres are similar.

4 lines
16.

The two figures are similar. Find the scale factor of the figure on the left to the figure on the right. Then find the ratio of surface areas and the ratio of volumes.

a)

2:9, 4:81, 8:729

b)

2:9, 4:9, 4:81

c)

2:9, 4:81, 14:6561

d)

2:9, 8:729, 4:81

17.
Are the two figures similar?
(If yes, what is the similarity ratio?)
a)
Yes; 5
b)
Yes; 9:6
c)
Yes; 1/3
d)
No
18.

The ratio of the volume of two spheres is 8:27. What is the ratio of their radii?

a)

2:3

b)

4:9

c)

3:4

d)

64:729

19.
If the volume of a right cylinder is 36π in3, and the height is 1, what is the diameter?
 
a)
6 in
b)
12 in
c)
36 in
d)
3 in
20.
What is the ratio of the surface areas from large to small. 
a)
49/16
b)
7/4
c)
42/24
d)
10/8
21.

What is the scale factor of the side lengths of the figure on the left to the figure on the right.

a)

3/1

b)

3240/120

c)

27/1

d)

9/1

22.
Find the volume of this square pyramid.
a)
214.8 m3
b)
586.7 m3
c)
1818.2 m3
d)
not enough information