[tex]511.05m^{2}[/tex] the area of the hot spring decrease .
Explanation:
Here we have A circular hot spring has a diameter of 110 meters. Over time, the diameter of the spring decreases by 3 meters. We need to calculate , how many square meters does the area of the hot spring decrease:
Area of circular hot spring initially = [tex]\pi r^{2}[/tex]
⇒ Area of circular hot spring initially = [tex]\pi r^{2}[/tex]
⇒ Area of circular hot spring initially = [tex]\pi (\frac{D}{2} )^{2} = \frac{\pi D^{2}}{4}[/tex]
⇒ Area of circular hot spring initially = [tex]\frac{\pi 110^{2}}{4} = 9498.5m^{2}[/tex]
Over time, the diameter of the spring decreases by 3 meters. Now,
Area = [tex]\pi (\frac{D-3}{2} )^{2} = \frac{\pi (D-3)^{2}}{4}[/tex]
Area = [tex]\frac{\pi (110-3)^{2}}{4} = 8987.45m^{2}[/tex]
Decrease in area :
⇒ [tex]9498.5m^{2} - 8987.45m^{2}[/tex]
⇒ [tex]511.05m^{2}[/tex]
∴ [tex]511.05m^{2}[/tex] the area of the hot spring decrease .
