The surface area of a shape is the amount of space on the shape
When the dimensions are quadrupled, the new surface area would be 16 times the initial surface area
<h3>How to determine the surface area</h3>The surface area of a rectangular prism is:
When quadrupled, we have:
Factor out 16
Substitute
The above means that:
The new surface area would be 16 times the initial surface area
Read more about surface areas at:
Answer: The central angle measures 135 degrees
Step-by-step explanation: We have been given an arc with length 9pi/2 feet and a radius of 6 feet. The arc is shown in the attached diagram (please see attachment). The central angle subtended by this arc is at point O and has been labeled angle X.
So if the diagram shows arc AB with length 9pi/2 and radius AO with length 6, we can use the formula to compute “Length of an arc” to arrive at the missing angle.
Length of an arc = X/360 x 2pi x radius
Substituting for the known values, our formula can now be re-written as
9pi/2 = X/360 x 2pi x6
By cross multiplication we now have
9pi/2pi x 6 = 2X/360
We simplify as much as possible by dividing all like terms, hence pi divides pi on the left side of the equation. Also 2 divides 360 on the right side of the equation.We now arrive at,
9/12 = X/180
Simplify even further and we have
3/4 = X/180
By cross multiplication we now have
(3 x 180)/4 = X
540/4 = X
135 = X
Therefore the central angle that intercepts the arc measures 135 degrees.
