Cylinders - Sample Math Practice Problems

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Complexity=1

Find the surface area and volume. Answer with proper units like m² and m³.
To represent m², use "sq m", etc. To answer with π, use "pi".
Sample area: 5π m² becomes "5pi sq m". Sample volume: 5π m³ becomes "5pi cu m".

1.	Surface Area = Volume =
2.	Surface Area = Volume =

Complexity=2

Find the surface area and volume. Answer with proper units like m² and m³.
To represent m², use "sq m", etc. To answer with π, use "pi".
Sample area: 5π m² becomes "5pi sq m". Sample volume: 5π m³ becomes "5pi cu m".

1.	Surface Area = Volume =
2.	Surface Area = Volume =

Answers

Complexity=1

Find the surface area and volume. Answer with proper units like m² and m³.
To represent m², use "sq m", etc. To answer with π, use "pi".
Sample area: 5π m² becomes "5pi sq m". Sample volume: 5π m³ becomes "5pi cu m".

#	Problem	Correct Answer	Your Answer
1		Surface Area = Volume =
Solution The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows: SA = 2πrh + 2πr2 SA = 2π × (3cm) × (2 cm) + 2π × (3 cm)2 SA = 2π × (6 cm2) + 2π × (9 cm2) SA = 12π cm2 + 18π cm2 SA = 30π cm2 The volume of a cylinder is the area of the base circle times the height of the cylinder. V = bh = πr2h V = π × (3 cm)2 × (2 cm) V = π × (9 cm2) × (2 cm) V = π × (18 cm3) V = 18π cm3

#	Problem	Correct Answer	Your Answer
2		Surface Area = Volume =
Solution The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows: SA = 2πrh + 2πr2 SA = 2π × (1cm) × (2 cm) + 2π × (1 cm)2 SA = 2π × (2 cm2) + 2π × (1 cm2) SA = 4π cm2 + 2π cm2 SA = 6π cm2 The volume of a cylinder is the area of the base circle times the height of the cylinder. V = bh = πr2h V = π × (1 cm)2 × (2 cm) V = π × (1 cm2) × (2 cm) V = π × (2 cm3) V = 2π cm3

Complexity=2

Find the surface area and volume. Answer with proper units like m² and m³.
To represent m², use "sq m", etc. To answer with π, use "pi".
Sample area: 5π m² becomes "5pi sq m". Sample volume: 5π m³ becomes "5pi cu m".

#	Problem	Correct Answer	Your Answer
1		Surface Area = Volume =
Solution The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows: SA = 2πrh + 2πr2 SA = 2π × (7yd) × (1 yd) + 2π × (7 yd)2 SA = 2π × (7 yd2) + 2π × (49 yd2) SA = 14π yd2 + 98π yd2 SA = 112π yd2 The volume of a cylinder is the area of the base circle times the height of the cylinder. V = bh = πr2h V = π × (7 yd)2 × (1 yd) V = π × (49 yd2) × (1 yd) V = π × (49 yd3) V = 49π yd3

#	Problem	Correct Answer	Your Answer
2		Surface Area = Volume =
Solution The surface area of a cylinder is the area of the bottom and top circles and the area of the side of the cylinder. This can be expressed as follows: SA = 2πrh + 2πr2 SA = 2π × (8m) × (4 m) + 2π × (8 m)2 SA = 2π × (32 m2) + 2π × (64 m2) SA = 64π m2 + 128π m2 SA = 192π m2 The volume of a cylinder is the area of the base circle times the height of the cylinder. V = bh = πr2h V = π × (8 m)2 × (4 m) V = π × (64 m2) × (4 m) V = π × (256 m3) V = 256π m3