Question

A parabolic listening device is shaped such that the depth of the bowl depends on its radius and can be represented by the curve D(r)= 0.145r^2. What is the radius when the depth is 8 inches? Round to the nearest thousandth of an inch

Answer 1

Answer : The radius of bowl is, 7.428 inches.

Step-by-step explanation :

As we are given that:

Depth of the bowl = D(r) = 0.145 r²

Given:

Depth of the bowl = D = 8 inches

Now put all the given values in the above expression, we get the radius of bowl.

$D(r)=0.145\times r^2$

$8\text{ inches}=0.145\times r^2$

$r^2=\frac{8\text{ inches}}{0.145}$

$r=\sqrt{\frac{8\text{ inches}}{0.145}}$

$r=7.428\text{ inches}$

Therefore, the radius of bowl is, 7.428 inches.