← Geometry

Geometry

Surface Area

Lesson

The surface area of a solid is the total area of all its outer faces. Imagine unfolding the solid flat — the area of that net is the surface area.

Formulas

  • Cube: 6s26 s^2
  • Rectangular prism: 2(ℓw+ℓh+wh)2(\ell w + \ell h + w h)
  • Cylinder: 2πr2+2πrh2\pi r^2 + 2\pi r h (top + bottom + side)
  • Sphere: 4πr24\pi r^2
  • Cone: πr2+πrℓ\pi r^2 + \pi r \ell (base + lateral, ℓ is slant height)
  • Square pyramid: b2+4⋅12bℓb^2 + 4 \cdot \tfrac{1}{2} b \ell

Use π≈3.14\pi \approx 3.14 throughout this topic.

Worked example

Cube with side 5:

SA=6⋅52=150\text{SA} = 6 \cdot 5^2 = 150

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Cube s=3\text{Cube } s = 3

Problem 2

Cube s=4\text{Cube } s = 4

Problem 3

Rect prism 2×3×4\text{Rect prism } 2 \times 3 \times 4

Problem 4

Sphere r=1 (π=3.14)\text{Sphere } r = 1 \ (\pi = 3.14)

Practice

Standard problems matching the lesson.

Problem 5

Cube s=5\text{Cube } s = 5

Problem 6

Cube s=2\text{Cube } s = 2

Problem 7

Rect prism 3×4×5\text{Rect prism } 3 \times 4 \times 5

Problem 8

Rect prism 1×2×3\text{Rect prism } 1 \times 2 \times 3

Problem 9

Cylinder r=3,h=10\text{Cylinder } r=3, h=10

Problem 10

Cylinder r=5,h=10\text{Cylinder } r=5, h=10

Problem 11

Cylinder r=1,h=5\text{Cylinder } r=1, h=5

Problem 12

Sphere r=3\text{Sphere } r=3

Problem 13

Sphere r=5\text{Sphere } r=5

Problem 14

Cone r=3,ℓ=5\text{Cone } r=3, \ell=5

Problem 15

Cone r=6,ℓ=10\text{Cone } r=6, \ell=10

Problem 16

Square pyramid base 4, slant 6\text{Square pyramid base 4, slant 6}

Problem 17

Cube s=10\text{Cube } s = 10

Problem 18

Cube s=1\text{Cube } s = 1

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Cube SA 54. Side?\text{Cube SA 54. Side?}

Problem 20

Cube SA 600. Side?\text{Cube SA 600. Side?}

Problem 21

Sphere SA 113.04. Radius?\text{Sphere SA 113.04. Radius?}

Problem 22

Cylinder r=2 SA 100.48. Height?\text{Cylinder } r=2 \text{ SA 100.48. Height?}

Problem 23

Cube SA 96. Edge?\text{Cube SA 96. Edge?}

Problem 24

Rect prism 2×4×6\text{Rect prism } 2 \times 4 \times 6

Problem 25

Square pyramid base 6, slant 5\text{Square pyramid base 6, slant 5}

Ask the tutor

Stuck on a concept? Want another example? Ask anything about this topic.

Type your own question below, or tap one of the suggestions. The tutor can re-explain the lesson, work through a specific problem with you, generate fresh practice tuned to where you are, or check your reasoning.

Quiz

Test yourself on this topic →

10 questions, no hints. About 5 minutes.