# A cone has a height of #12 cm# and its base has a radius of #8 cm#. If the cone is horizontally cut into two segments #4 cm# from the base, what would the surface area of the bottom segment be?

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:.Pythagoras:

:.*r*L#

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:.Total S.A.

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:.S.A. top part

S.A. top part

S.A. top part

S.A. top part

:.S.A. Bottom part

:.S.A. Bottom part

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Apply the formula for the surface area (

Plug in the numbers and we get:

Which is approximately

You might think about this formula by imaging the products of an *exploded* (or unrolled) cylinder.

The cylinder would include three surfaces: a pair of identical circles of radii of

Now we find the area formula for each of the component:

Adding them to find an expression for the surface area of the cylinder:

Factor out

*Notice that since each cylinder has two caps, there are two*

Reference and Image Attributions:

Niemann, Bonnie, and Jen Kershaw. “Surface Area of Cylinders.” CK-12 Foundation, CK-12 Foundation, 8 Sept. 2016, www.ck12.org/geometry/surface-area-of-cylinders/lesson/Surface-Area-of-Cylinders-MSM7/?referrer=concept_details.

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