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WorksheetsRatios of perimeter/area/volume of 2-D and 3-D figures
Total questions: 25
Worksheet time: 13mins
Name
Class
Date
1.
Cylinder A is similar to cylinder B with a perimeter ratio A:B of 3:9. What is the ratio of the surface areas?
a)
27:729
b)
1:3
c)
9:81
d)
9:3
2.
The scale factor of a model car is 1:7. If the actual car is 18 ft long and 8 ft wide, how long and wide in feet is the model car to the nearest tenth?
a)
l = 4 ft, w = 1.5 ft
b)
l = 3.4 ft, w = 2.3 ft
c)
l = 9 ft, w = 3 ft
d)
l = 2.6 ft, w = 1.2 ft
3.
Rectangle A is similar to rectangle B. The ratio of the areas A:B is 25:121. What is the ratio of the perimeters?
a)
121:1331
b)
5:11
c)
11:5
d)
5:1
4.
You are sketching a ladybug and the scale factor of the ladybug to your sketch is 7:23. If the ladybug is 6 mm in length and 4 mm, what is the length and width of your sketch to the nearest tenth?
a)
l = 19.7 mm,
w = 13.1 mm
w = 13.1 mm
b)
l = 13.1 mm,
w = 19.7 mm
w = 19.7 mm
c)
l = 23 mm,
w = 15 mm
w = 15 mm
d)
l = 15 mm,
w = 23 mm
w = 23 mm
5.
Sphere C has a volume of 343 and sphere D has a volume of 512. Assuming the two solids are similar, what is the ratio of the surface areas C:D?
a)
49:64
b)
7:8
c)
9:25
d)
16:49
6.
Find the ratio of the radii if the ratio of the areas is 49:361
a)
7:9
b)
19:7
c)
7:19
d)
9:6
7.
Rectangle X and rectangle Y are similar with a scale factor of 5:7. What are the ratios of the perimeters and areas X:Y?
a)
7:5, 49:25
b)
5:7, 25:49
c)
125:343, 25:49
d)
49:16, 16:25
8.
Find the volume of rectangle B if the scale factor of rectangle A to B is 11:6
a)
V = 121
b)
V = 35.3
c)
V = 13.54
d)
V = 216
9.
Cone A is similar to cone B and the ratio of their surface areas is 36:64
A to B. What is the ratio of the volume and what is the scale factor?
A to B. What is the ratio of the volume and what is the scale factor?
a)
V = 216:729,
SF = 6:8
SF = 6:8
b)
V = 729:216,
SF = 8:6
SF = 8:6
c)
V = 216:512,
SF = 8:6
SF = 8:6
d)
V = 216:512,
SF = 6:8
SF = 6:8
10.
There are two cylinders. The small cylinder has a height of 24 cm. If the ratios of the surface areas are 16:25, what is the height of the taller cylinder?
a)
80 cm
b)
30 cm
c)
60 cm
d)
35 cm
11.
Two spheres have radii in a ratio of 3:4. What are the ratios of their volumes?
a)
9:16
b)
64:27
c)
4:3
d)
27:64
12.
Circle T has a circumference of 81.68 and Circle S has a diameter of 8. How many times bigger is the area of Circle T than S?
a)
1.5
b)
2.64
c)
3
d)
2.1
13.
Pyramid X is similar to Pyramid Y. The surface area of pyramid X is 135cm², and the surface area of pyramid Y is 240cm². If the volume of Pyramid X is 189cm³, then what is the volume of Pyramid Y?
a)
336 cm³
b)
409 cm³
c)
340 cm³
d)
198 cm³
14.
If Jake has an ice cream cone with a lateral of 5 in and a radius of 1.2 in, and Matthew has an ice cream cone with a lateral of 3 and a radius of .6 in, (using surface area) how much bigger is Jake's cone than Matthew's?
a)
19
b)
11.7 in
c)
2 in
d)
16.6 in
15.
What is the ratio for area?
a)
a:b
b)
a^2:b^3
c)
a^2:b^2
d)
b:a
16.
Find the ratio of the volume of Dad's mug to Mom's mug if Dad's volume is 164.64 and Mom's is 50.26? (simplify the ratio)
a)
3.375:1
b)
7:3
c)
164.64:50.26
d)
50.26:164.64
17.
Are 2 rectangular prisms similar is A has l = 3, w = 5, and h = 4 and B has l = 4.5, w = 7.5, h = 6?
a)
No
b)
Yes
18.
Rectangle A has a volume of 857.375 while Rectangle B has a volume of 27. What is the scale factor of perimeter A to B to the nearest tenth?
a)
4:1
b)
9:3
c)
27:857.4
d)
3:2
19.
What is the scale factor of 2 rectangular prisms if the ratio of the volumes is 512:84 A to B? (rounded to the nearest whole)
a)
2
b)
1:2
c)
3
d)
2:5
20.
If Rectangular Prism A has l=6, w=9, h=8 and Rectangular Prism B has l=2, w=3, h=4, are they similar?
a)
Yes
b)
No
21.
Two right cylinders are similar and the surface areas are 24π and 96π. What is the ratio of the volumes of the cylinders?
a)
1:3
b)
3
c)
1:8
d)
5
22.
Two cubes have volumes of 64 cubic feet and 216 cubic feet, what is the ratio of the surface areas?
a)
1:4
b)
5:4
c)
9:4
d)
4:9
23.
The ratio between the perimeters of cube A and B is 2:3, A has a side length 9, what is the volume of cube B?
a)
2,460.375
b)
1,449.011
c)
94.503
d)
1
24.
Which set of dimensions corresponds to a right cylinder that is similar to a cylinder with a radius of 5 and height of 9?
a)
r=2
h=5
h=5
b)
r=3
h=7
h=7
c)
r=10
h=19
h=19
d)
r=15
h=27
h=27
25.
Solid A is similar to Solid B. What is the scale factor if the surface area of Solid A is 208 and B is 52?
a)
2:1
b)
1:2
c)
3:4
d)
4:3
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