MAP 4C
WS 4.6
Optimization of Rectangular Prisms and Cylinders
Show all of your work in your notebook.
For all questions, round your answer to the nearest tenth of a unit when necessary.
1. Each of these square-based prisms has volume 64 cm3.
a)
b)
c)
Find the height of each prism.
Find the surface area of each prism.
Order the prisms from least to greatest surface area.
2. A square-based prism has volume 512 cm3.
a)
b)
What are the possible whole-number dimensions of the prism?
Which dimensions produce the prism with the least surface area?
3. Find the dimensions of the square-based prism with minimum surface area, given each volume.
a) 216 cm3
b) 864 cm3
c) 111 cm3
d) 1331 cm3
4. Each square-based prism has surface area 216 cm2.
a)
b)
Find the volume of each prism.
Order the prisms from greatest to least volume.
5. Find the dimensions of the square-based prism with maximum volume, given each surface area.
a) 294 cm2
b) 486 cm2
c) 1176 cm2
d) 1350 cm2
e) 497 cm2
f) 662 cm2
6. Each cylinder has surface area 75.4 cm2. Order the cylinders from greatest to least volume.
7. Find the radius and height of the cylinder with maximum volume, given the surface area.
a) 250 cm2
c) 40 cm2
e) 750 cm2
b)
d)
f)
500 cm2
475 cm2
1000 cm2
8. Each cylinder has volume 50.3 cm3.
a)
b)
c)
Find the height of each cylinder.
Find the surface area of each cylinder.
Order the cylinders from least to greatest surface area.
9. Each cylinder has volume 402 cm3. Order the cylinders from least to greatest surface area.
10. Find the radius and height of the cylinder with minimum surface area, given the volume.
a) 1500 cm3
c) 80 cm3
e) 650 cm3
b) 400 cm3
d) 12 cm3
f ) 440 cm3
Answers
1.
a)
b)
c)
a)
A: 16 cm; B: 4 cm; C: 1 cm
A: 136 cm2; B: 96 cm2; C: 160 cm2
B, A, C
2.
8 by 8 by 8, 16 by 16 by 2, 4 by 4 by 32,
1 by 1 by 512, 2 by 2 by 128
b) 8 by 8 by 8
3. a) 6 by 6 by 6
b) 9.5 by 9.5 by 9.5
c) 4.8 by 4.8 by 4.8
d) 11 by 11 by 11
4. a) A: 40 cm3; B: 216 cm3; C: 184 cm3
b) B, C, A
5. a) 7 cm by 7 cm by 7 cm
b) 9 cm by 9 cm by 9 cm
c) 14 cm by 14 cm by 14 cm
d) 15 cm by 15 cm by 15 cm
e) 9.1 cm by 9.1 cm by 9.1 cm
f ) 10.5 cm by 10.5 cm by 10.5 cm
6.
B, A, C
7.
a) 7 cm by 7 cm by 7 cm
b) 9 cm by 9 cm by 9 cm
c) 14 cm by 14 cm by 14 cm
d) 15 cm by 15 cm by 15 cm
e) 9.1 cm by 9.1 cm by 9.1 cm
f ) 10.5 cm by 10.5 cm by 10.5 cm
8. a) A: 8.2 cm; B: 1 cm; C: 4 cm
b) A: 84.4 cm2; B: 125.7 cm2; C: 75.4 cm2
c) C, A, B
9. B, C, A
10. a) r = 6.2 cm; h = 12.4 cm
b) r = 4 cm; h = 8 cm
c) r = 2.3 cm; h = 4.7 cm
d) r = 1.2 cm; h = 2.5 cm
e) r = 4.7 cm; h = 9.4 cm
f ) r = 4.1 cm; h = 8.2 cm