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## Rectangular Solids 2 - 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=3, Mode=word

 1.   The surface area of a rectangular solid is 24 m2. The lengths of two of the sides are 2 m and 2 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 6 m3. The length is 3 m and the height is 2 m. What is the width? w =

### Complexity=4, Mode=word

 1.   The surface area of a rectangular solid is 54 m2. The lengths of two of the sides are 3 m and 3 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 48 yd3. The length is 3 yd and the width is 4 yd. What is the height? h =

### Complexity=6, Mode=word

 1.   The surface area of a rectangular solid is 130 ft2. The lengths of two of the sides are 5 ft and 4 ft. What is the length of the other side? length = 2.   The volume of a rectangular solid is 54 in3. The length is 6 in and the height is 3 in. What is the width? w =

### Complexity=8, Mode=word

 1.   The surface area of a rectangular solid is 144 yd2. The lengths of two of the sides are 3 yd and 6 yd. What is the length of the other side? length = 2.   The volume of a rectangular solid is 54 m3. The width is 6 m and the height is 3 m. What is the length? L =

### Complexity=10, Mode=word

 1.   The surface area of a rectangular solid is 258 m2. The lengths of two of the sides are 5 m and 6 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 112 cm3. The width is 7 cm and the height is 4 cm. What is the length? L =

### Complexity=12, Mode=word

 1.   The surface area of a rectangular solid is 190 ft2. The lengths of two of the sides are 9 ft and 2 ft. What is the length of the other side? length = 2.   The volume of a rectangular solid is 162 yd3. The length is 6 yd and the height is 3 yd. What is the width? w =

### Complexity=3, Mode=word

1The surface area of a rectangular solid is 24 m2.
The lengths of two of the sides are 2 m and 2 m.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
24m2 = (2 × 2m × 2m) + (2 × 2m × h) + (2 × 2m × h)
24m2 = 8m2 + (4 m)h + (4 m)h
16m2 = (8 m)h
2m = h
2The volume of a rectangular solid is 6 m3.
The length is 3 m and the height is 2 m. What is the width?
w =
Solution
V = Lwh
6m3 = 3 × w × 2m
3m2 = 3m × w
1m = w

### Complexity=4, Mode=word

1The surface area of a rectangular solid is 54 m2.
The lengths of two of the sides are 3 m and 3 m.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
54m2 = (2 × 3m × 3m) + (2 × 3m × h) + (2 × 3m × h)
54m2 = 18m2 + (6 m)h + (6 m)h
36m2 = (12 m)h
3m = h
2The volume of a rectangular solid is 48 yd3.
The length is 3 yd and the width is 4 yd. What is the height?
h =
Solution
V = Lwh
48yd3 = 3yd × 4yd × h
16yd2 = 4yd × h
4yd = h

### Complexity=6, Mode=word

1The surface area of a rectangular solid is 130 ft2.
The lengths of two of the sides are 5 ft and 4 ft.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
130ft2 = (2 × 5ft × 4ft) + (2 × 5ft × h) + (2 × 4ft × h)
130ft2 = 40ft2 + (10 ft)h + (8 ft)h
90ft2 = (18 ft)h
5ft = h
2The volume of a rectangular solid is 54 in3.
The length is 6 in and the height is 3 in. What is the width?
w =
Solution
V = Lwh
54in3 = 6 × w × 3in
18in2 = 6in × w
3in = w

### Complexity=8, Mode=word

1The surface area of a rectangular solid is 144 yd2.
The lengths of two of the sides are 3 yd and 6 yd.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
144yd2 = (2 × 3yd × 6yd) + (2 × 3yd × h) + (2 × 6yd × h)
144yd2 = 36yd2 + (6 yd)h + (12 yd)h
108yd2 = (18 yd)h
6yd = h
2The volume of a rectangular solid is 54 m3.
The width is 6 m and the height is 3 m. What is the length?
L =
Solution
V = Lwh
54m3 = L × 6m × 3m
18m2 = L × 6m
3m = L

### Complexity=10, Mode=word

1The surface area of a rectangular solid is 258 m2.
The lengths of two of the sides are 5 m and 6 m.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
258m2 = (2 × 5m × 6m) + (2 × 5m × h) + (2 × 6m × h)
258m2 = 60m2 + (10 m)h + (12 m)h
198m2 = (22 m)h
9m = h
2The volume of a rectangular solid is 112 cm3.
The width is 7 cm and the height is 4 cm. What is the length?
L =
Solution
V = Lwh
112cm3 = L × 7cm × 4cm
28cm2 = L × 7cm
4cm = L

### Complexity=12, Mode=word

1The surface area of a rectangular solid is 190 ft2.
The lengths of two of the sides are 9 ft and 2 ft.
What is the length of the other side?
length =
Solution
Surface Area = 2Lw + 2Lh + 2wh
Pick h as the unknown (your choice doesn't matter)
190ft2 = (2 × 9ft × 2ft) + (2 × 9ft × h) + (2 × 2ft × h)
190ft2 = 36ft2 + (18 ft)h + (4 ft)h
154ft2 = (22 ft)h
7ft = h