The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by $r ( t ) = 2.25 \sqrt { t }$ , where r is the radius in meters and t is the time in hours since contamination.
Find a function that gives the area A of the circular lake in terms of the time since the spread began.

A) $A \circ r ( t ) = 5.0625 \pi \sqrt { t }$
B) $A \circ r ( t ) = 2.25 \pi t$
C) $A \circ r ( t ) = 5.0625 t$
D) $A \circ r ( t ) = 5.0625 \sqrt { t }$
E) $A \circ r ( t ) = 5.0625 \pi t$

Question

The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by $r ( t ) = 2.25 \sqrt { t }$ , where r is the radius in meters and t is the time in hours since contamination.  
Find a function that gives the area A of the circular lake in terms of the time since the spread began.
 
A) $A \circ r ( t ) = 5.0625 \pi \sqrt { t }$
B) $A \circ r ( t ) = 2.25 \pi t$
C) $A \circ r ( t ) = 5.0625 t$
D) $A \circ r ( t ) = 5.0625 \sqrt { t }$
E) $A \circ r ( t ) = 5.0625 \pi t$

Quizplus · Accepted Answer

The area of a circle is given by $A = \pi r^2$. Substituting the given $r(t) = 2.25\sqrt{t}$ into this formula, we get $A = \pi (2.25\sqrt{t})^2 = \pi (5.0625t) = 5.0625 \pi t$.

The Spread of a Contaminant Is Increasing in a Circular r(t)=2.25tr ( t ) = 2.25 \sqrt { t }r(t)=2.25t​

The Spread of a Contaminant Is Increasing in a Circular $r ( t ) = 2.25 \sqrt { t }$