Question

the steps in a spiral staircase are shaped like sectors represented by the diagram. how large is each stepping area? complete each line in the solution. move one answer to each box. a = 1/2( )^2( ) a = { }ft.^2

Explanation:

Step1: Recall sector - area formula

The area formula for a sector of a circle in radians is $A=\frac{1}{2}r^{2}\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle of the sector in radians.

Step2: Identify radius and angle

We need to know the values of the radius $r$ and the central - angle $\theta$ from the given diagram. Let's assume the radius of the sector (the distance from the center of the spiral to the outer edge of the step) is $r$ and the central - angle of the sector is $\theta$ (in radians).

Step3: Substitute values into formula

If we know the values of $r$ and $\theta$, we substitute them into the formula $A = \frac{1}{2}r^{2}\theta$.

Answer:

We need the values of $r$ and $\theta$ from the diagram to give a numerical answer. If the radius is $r$ and the central - angle in radians is $\theta$, then $A=\frac{1}{2}r^{2}\theta$ square feet.