Surface area and Volume of a candy cane?

Question

Surface area and Volume of a candy cane? anyone?

how do you find the Surface area and Volume of a candy cane?

Answer 1

candy canes range from small to very large

Answer 2

A candy cane can be broken down to a cylindral section and a half a torus. The volume and area of a cylinder are:

V = pi r^2 h
A = 2 pi r h

where r is the radius and h is the length

The volume and area of a torus on the other hand are:

V = 2 pi^2 r^2 R
A = 4 pi^2 r R

where r is the radius and R is the radius of curved axis of the torus.

For the ends of the candy cane, we add the circles of area A, where

A = pi r^2

The total volume and area of the candy cane, from these, comes to:

V = pi r^2 h + pi^2 r^2 R
A = 2 pi r h + 2 pi^2 r R + 2 pi r^2

Recall that for the top of the candy cane, it's half of a torus. And the other answers given have left out the ends of the candy cane.

Answer 3

As kellenraid alluded to, a candy cane is a bent cylinder. We know the volume of a (right) cylinder is v=pi r^2 * h, where r is the radius of the cylinder (or, half the diameter) and h is the length of the candy cane. To find the length, you can take a piece of string, follow the shape of the candy cane, then pull it straight and measure with a ruler. The surface area of the candy cane is just a=2 pi r * h.

Another way to find the volume of the candy cane is to submerge it in a liquid. It may dissolve a little bit in water, but hopefully not too much. Measure the volume of the water (or other liquid) before and after putting the candy cane in.

Answer 4

The cane is crooked. So to determine the volume, then take the center and determine the length. The diameter is measureable. The volume is
V = pi(radius^2)length of center.
Surface area = pi(2r)length of center