Math Skill: Rectangular Solids 2
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Rectangular Solids 2

To master this topic, you should understand the volume and surface area formulas for rectangular solids.
For review the Rectangular Solids topic, see here.

Example 1: Volume

The volume of a rectangular solid is 72 ft3.
The length is 6 ft and the height is 3 ft. What is the width?
w =

Use the volume formula and plug in what you know.
Then solve for the unknown.

We are solving for the width, w.
The answer is w = .

Example 2: Surface Area

The surface area of a rectangular solid is 52 cm2.
The lengths of two of the sides are 4 cm and 2 cm.
What is the length of the other side?
length =

Use the surface area formula and plug in what you know.
Then solve for the unknown.

Assign width = 4 cm and height = 2 cm.
We are solving for the length, l.
The answer is length = .

### Complexity=3, Mode=word

 1.   The surface area of a rectangular solid is 22 m2. The lengths of two of the sides are 1 m and 3 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 2 yd3. The length is 1 yd and the width is 1 yd. What is the height? h =

### Complexity=4, Mode=word

 1.   The surface area of a rectangular solid is 52 m2. The lengths of two of the sides are 4 m and 3 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 6 yd3. The width is 1 yd and the height is 2 yd. What is the length? L =

### Complexity=6, Mode=word

 1.   The surface area of a rectangular solid is 62 m2. The lengths of two of the sides are 2 m and 3 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 60 in3. The width is 5 in and the height is 4 in. What is the length? L =

### Complexity=8, Mode=word

 1.   The surface area of a rectangular solid is 122 m2. The lengths of two of the sides are 7 m and 3 m. What is the length of the other side? length = 2.   The volume of a rectangular solid is 80 ft3. The length is 8 ft and the height is 2 ft. What is the width? w =

### Complexity=10, Mode=word

 1.   The surface area of a rectangular solid is 112 ft2. The lengths of two of the sides are 8 ft and 2 ft. What is the length of the other side? length = 2.   The volume of a rectangular solid is 240 yd3. The length is 6 yd and the height is 8 yd. What is the width? w =

### Complexity=12, Mode=word

 1.   The surface area of a rectangular solid is 344 cm2. The lengths of two of the sides are 10 cm and 6 cm. What is the length of the other side? length = 2.   The volume of a rectangular solid is 72 in3. The width is 2 in and the height is 3 in. What is the length? L =

### Complexity=3, Mode=word

1The surface area of a rectangular solid is 22 m2.
The lengths of two of the sides are 1 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)
22m2 = (2 × 1m × 3m) + (2 × 1m × h) + (2 × 3m × h)
22m2 = 6m2 + (2 m)h + (6 m)h
16m2 = (8 m)h
2m = h
2The volume of a rectangular solid is 2 yd3.
The length is 1 yd and the width is 1 yd. What is the height?
h =
Solution
V = Lwh
2yd3 = 1yd × 1yd × h
2yd2 = 1yd × h
2yd = h

### Complexity=4, Mode=word

1The surface area of a rectangular solid is 52 m2.
The lengths of two of the sides are 4 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)
52m2 = (2 × 4m × 3m) + (2 × 4m × h) + (2 × 3m × h)
52m2 = 24m2 + (8 m)h + (6 m)h
28m2 = (14 m)h
2m = h
2The volume of a rectangular solid is 6 yd3.
The width is 1 yd and the height is 2 yd. What is the length?
L =
Solution
V = Lwh
6yd3 = L × 1yd × 2yd
3yd2 = L × 1yd
3yd = L

### Complexity=6, Mode=word

1The surface area of a rectangular solid is 62 m2.
The lengths of two of the sides are 2 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)
62m2 = (2 × 2m × 3m) + (2 × 2m × h) + (2 × 3m × h)
62m2 = 12m2 + (4 m)h + (6 m)h
50m2 = (10 m)h
5m = h
2The volume of a rectangular solid is 60 in3.
The width is 5 in and the height is 4 in. What is the length?
L =
Solution
V = Lwh
60in3 = L × 5in × 4in
15in2 = L × 5in
3in = L

### Complexity=8, Mode=word

1The surface area of a rectangular solid is 122 m2.
The lengths of two of the sides are 7 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)
122m2 = (2 × 7m × 3m) + (2 × 7m × h) + (2 × 3m × h)
122m2 = 42m2 + (14 m)h + (6 m)h
80m2 = (20 m)h
4m = h
2The volume of a rectangular solid is 80 ft3.
The length is 8 ft and the height is 2 ft. What is the width?
w =
Solution
V = Lwh
80ft3 = 8 × w × 2ft
40ft2 = 8ft × w
5ft = w

### Complexity=10, Mode=word

1The surface area of a rectangular solid is 112 ft2.
The lengths of two of the sides are 8 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)
112ft2 = (2 × 8ft × 2ft) + (2 × 8ft × h) + (2 × 2ft × h)
112ft2 = 32ft2 + (16 ft)h + (4 ft)h
80ft2 = (20 ft)h
4ft = h
2The volume of a rectangular solid is 240 yd3.
The length is 6 yd and the height is 8 yd. What is the width?
w =
Solution
V = Lwh
240yd3 = 6 × w × 8yd
30yd2 = 6yd × w
5yd = w

### Complexity=12, Mode=word

1The surface area of a rectangular solid is 344 cm2.
The lengths of two of the sides are 10 cm and 6 cm.
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)
344cm2 = (2 × 10cm × 6cm) + (2 × 10cm × h) + (2 × 6cm × h)
344cm2 = 120cm2 + (20 cm)h + (12 cm)h
224cm2 = (32 cm)h
7cm = h