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

Solve. Answer with proper units.

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

Solve. Answer with proper units.

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

Solve. Answer with proper units.

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

Solve. Answer with proper units.

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

Solve. Answer with proper units.

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

Solve. Answer with proper units.

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 =

Answers

Complexity=3, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 2yd³ = 1yd × 1yd × h 2yd² = 1yd × h 2yd = h

Complexity=4, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 6yd³ = L × 1yd × 2yd 3yd² = L × 1yd 3yd = L

Complexity=6, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 60in³ = L × 5in × 4in 15in² = L × 5in 3in = L

Complexity=8, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 80ft³ = 8 × w × 2ft 40ft² = 8ft × w 5ft = w

Complexity=10, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 240yd³ = 6 × w × 8yd 30yd² = 6yd × w 5yd = w

Complexity=12, Mode=word

Solve. Answer with proper units.

#	Problem	Correct Answer	Your Answer
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 =
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

#	Problem	Correct Answer	Your Answer
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 =
Solution V = Lwh 72in³ = L × 2in × 3in 24in² = L × 2in 12in = L

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