Before you read

Answer first — see what you already know.

A gift box is a cube with edge length 4 cm. How much wrapping paper is needed to cover all six faces?

A
64 cm $^{2}$
B
96 cm $^{2}$
C
128 cm $^{2}$
D
256 cm $^{2}$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A spherical globe has radius 5 inches. What is the surface area of the globe?

A
$25 π$ in $^{2}$
B
$50 π$ in $^{2}$
C
$100 π$ in $^{2}$
D
$500 π$ in $^{2}$

Check your answer

Answer:

Theory

Surface Area Formulas

Rectangular prism: $SA = 2(lw + lh + wh)$

Rectangular prism surface area

Cube: $SA = 6s^2$

Cylinder: $SA = 2\pi r^2 + 2\pi rh$ (two circles + lateral surface)

Cylinder surface area

Sphere: $SA = 4\pi r^2$

Surface area = the total area of all outer surfaces.

Example 1

A cylinder has radius 3 cm and height 8 cm. What is its total surface area?

Two circles: $2\pi(3)^2 = 18\pi$

Lateral: $2\pi(3)(8) = 48\pi$

Total: $18\pi + 48\pi = 66\pi$ cm $^{2}$

66\pi \approx 207.3

^{2}

Strategy

SAT Pro Tip

The lateral surface of a cylinder, when 'unrolled', is a rectangle with width $= 2\pi r$ (circumference) and height $= h$ . This helps you visualize why the formula is $2\pi rh$ .

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