The volume of a cylinder (think about the volume of a can) is given by V = £kr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.

a)

To find the value of k that makes the equation V = £kr^2h hold true for a can with a volume of 100 cubic centimeters, we need to use the given information.

The equation for the volume of a cylinder is V = £kr^2h, where V is the volume, r is the radius, h is the height, and £k is a constant. We are given that the volume of the can is 100 cubic centimeters.

Substituting the given values into the equation, we have:

100 = £kr^2h

Since we want to find the value of k, we need to rearrange the equation to solve for k. First, divide both sides of the equation by r^2h:

100/(r^2h) = £k

Now, we know that the volume of the can is 100 cubic centimeters, so we need to know the values of r and h to calculate k. Once we have the values of r and h, we substitute them into the equation to find the value of k.

For example, let's say the radius of the can is 5 centimeters and the height is 4 centimeters. Substituting these values into the equation, we have:

100/(5^2 * 4) = £k

100/100 = £k

1 = £k

So, in this case, k would be equal to 1.

To find the value of k for a different can, you need to know the values of r and h and substitute them into the equation. The value of k will vary depending on the dimensions of the specific can.