## 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.   10 m3 = cm3 2.   3000 mm3 = cm3

### Complexity=10, Mode=english

Do the following conversions. Round to nearest tenth where necessary.
 1.   8640 in3 = ft3 2.   9 ft3 = in3

### Complexity=10, Mode=mixed

Do the following conversions. Round to nearest tenth where necessary.
 1.   1152 in2 = ft2 2.   5 m3 = cm3

### Complexity=10, Mode=complex

Do the following conversions. Round to nearest tenth where necessary.
 1.   7.8 yd3 = m3 2.   9 ft3 = mm3

### Complexity=10, Mode=metric

Do the following conversions. Round to nearest tenth where necessary.
110 m3 = cm3
Solution

10 m3 ×
( 100 cm
1 m
)
 3
= 10 m3 ×
 1,000,000 cm31 m3
= 10000000 cm3
23000 mm3 = cm3
Solution

3000 mm3 ×
( 1 cm
10 mm
)
 3
= 3000 mm3 ×
 1 cm31,000 mm3
= 3 cm3

### Complexity=10, Mode=english

Do the following conversions. Round to nearest tenth where necessary.
18640 in3 = ft3
Solution

8640 in3 ×
( 1 ft
12 in
)
 3
= 8640 in3 ×
 1 ft31,728 in3
= 5 ft3
29 ft3 = in3
Solution

9 ft3 ×
( 12 in
1 ft
)
 3
= 9 ft3 ×
 1,728 in31 ft3
= 15552 in3

### Complexity=10, Mode=mixed

Do the following conversions. Round to nearest tenth where necessary.
11152 in2 = ft2
Solution

1152 in2 ×
( 1 ft
12 in
)
 2
= 1152 in2 ×
 1 ft2144 in2
= 8 ft2
25 m3 = cm3
Solution

5 m3 ×
( 100 cm
1 m
)
 3
= 5 m3 ×
 1,000,000 cm31 m3
= 5000000 cm3

### Complexity=10, Mode=complex

Do the following conversions. Round to nearest tenth where necessary.
17.8 yd3 = m3
Solution

7.8 yd3 ×
( 1 m
1.094 yd
)
 3
= 7.8 yd3 ×
 1 m31.308 yd3
= 6 m3
29 ft3 = mm3
Solution

9 ft3 ×
( 304.8 mm
1 ft
)
 3
= 9 ft3 ×
 28,316,846.592 mm31 ft3
= 254851619.3 mm3