Answer:
The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex] when the radius is 13 cm
Step-by-step explanation:
Given:
radius of the pool increases at a rate of 8 cm/min
To Find:
How fast is the area of the pool increasing when the radius is 13 cm ?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A =[tex]\pi r^2[/tex]-----------------------------(1)
The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]
we have to find [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and r = 13cm
substituting the values
[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]
[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]
[tex]\frac{d A}{d t}= 208 \pi[/tex]
[tex]\frac{d A}{d t}=653.12[/tex]
Answer:
208pi cm^2/min
Step-by-step explanation:Take the derivative of the formula for Area and substitute the values
