To find the number of layers in the cake, we need to use the formula for the volume of a cylinder. The formula is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the height of the cake is centimeters and the radius is , we can substitute these values into the formula.

V = π( )^2( )

Since each cake layer has a volume of approximately cubic centimeters, we can set up an equation:

V = cubic centimeters

π( )^2( ) = cubic centimeters

Now we can solve for the number of layers. We can rearrange the equation to solve for :

( )^2( ) = / π

Taking the square root of both sides:

( )^2 = / π

Simplifying:

( )^2 =

Taking the square root again:

= √( )

Calculating the square root:

=

Therefore, the cake has approximately layers.

Question

To find the number of layers in the cake, we need to use the formula for the volume of a cylinder. The formula is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the height of the cake is  centimeters and the radius is , we can substitute these values into the formula.

V = π( )^2( )

Since each cake layer has a volume of approximately  cubic centimeters, we can set up an equation:

V =  cubic centimeters

π( )^2( ) =  cubic centimeters

Now we can solve for the number of layers. We can rearrange the equation to solve for :

( )^2( ) =  / π

Taking the square root of both sides:

( )^2 =  / π

Simplifying:

( )^2 =

Taking the square root again:

= √(   )

Calculating the square root:

=

Therefore, the cake has approximately  layers.

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