Question

7. A circular hot spring has a diameter of 110 meters. Over time, the diameter

Answer 1

$511.05m^{2}$ 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 = $\pi r^{2}$

⇒ Area of circular hot spring initially = $\pi r^{2}$

⇒ Area of circular hot spring initially = $\pi (\frac{D}{2} )^{2} = \frac{\pi D^{2}}{4}$

⇒ Area of circular hot spring initially = $\frac{\pi 110^{2}}{4} = 9498.5m^{2}$

Over time, the diameter  of the spring decreases by 3 meters. Now,

Area = $\pi (\frac{D-3}{2} )^{2} = \frac{\pi (D-3)^{2}}{4}$

Area = $\frac{\pi (110-3)^{2}}{4} = 8987.45m^{2}$

Decrease in area :

⇒ $9498.5m^{2} - 8987.45m^{2}$

⇒ $511.05m^{2}$

∴ $511.05m^{2}$ the  area of the hot spring decrease .