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## Area and Volume Conversions - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=10, Mode=metric

Do the following conversions. Round to nearest tenth where necessary.

 1.   6 cm3 = mm3 2.   3000000 cm3 = m3

### Complexity=10, Mode=english

Do the following conversions. Round to nearest tenth where necessary.

 1.   8 ft3 = in3 2.   2 ft2 = in2

### Complexity=10, Mode=mixed

Do the following conversions. Round to nearest tenth where necessary.

 1.   6 km3 = m3 2.   500 mm2 = cm2

### Complexity=10, Mode=complex

Do the following conversions. Round to nearest tenth where necessary.

 1.   7000000000000 mm2 = km2 2.   2 cm2 = mm2

### Complexity=10, Mode=metric

Do the following conversions. Round to nearest tenth where necessary.

16 cm3 = mm3
Solution

6 cm3 ×
( 10 mm
1 cm
)
 3
= 6 cm3 ×
 1,000 mm31 cm3
= 6000 mm3
23000000 cm3 = m3
Solution

3000000 cm3 ×
( 1 m
100 cm
)
 3
= 3000000 cm3 ×
 1 m31,000,000 cm3
= 3 m3

### Complexity=10, Mode=english

Do the following conversions. Round to nearest tenth where necessary.

18 ft3 = in3
Solution

8 ft3 ×
( 12 in
1 ft
)
 3
= 8 ft3 ×
 1,728 in31 ft3
= 13824 in3
22 ft2 = in2
Solution

2 ft2 ×
( 12 in
1 ft
)
 2
= 2 ft2 ×
 144 in21 ft2
= 288 in2

### Complexity=10, Mode=mixed

Do the following conversions. Round to nearest tenth where necessary.

16 km3 = m3
Solution

6 km3 ×
( 1000 m
1 km
)
 3
= 6 km3 ×
 1,000,000,000 m31 km3
= 6000000000 m3
2500 mm2 = cm2
Solution

500 mm2 ×
( 1 cm
10 mm
)
 2
= 500 mm2 ×
 1 cm2100 mm2
= 5 cm2

### Complexity=10, Mode=complex

Do the following conversions. Round to nearest tenth where necessary.

17000000000000 mm2 = km2
Solution

7000000000000 mm2 ×
( 1 km
1000000 mm
)
 2
= 7000000000000 mm2 ×
 1 km21,000,000,000,000 mm2
= 7 km2
22 cm2 = mm2
Solution

2 cm2 ×
( 10 mm
1 cm
)
 2
= 2 cm2 ×
 100 mm21 cm2
= 200 mm2