Question

If the area of a circle increases at a uniform rate, then its perimeter varies

• A. directly as its radius
• B. inversely as its radius
• C. directly as the square of its radius
• D. inversely as the square of the radius

Answer 1

Answer: (A)

directly as its radius

Answer 2

Area of circle = $\pi r^2$ and perimeter = $2\pi r$
Let $f(r) = \pi r^2 \Rightarrow \: f'(r) = 2 \pi r$
$f(r)$ is increases $\Rightarrow \:\: f'(r) \geq 0$
Now $f"(r) = 2\pi > 0$
$\Rightarrow \: f' (r)$ is also an increasing function
$\Rightarrow \:\: f' (r)$ varies directly as its radius