Question

The rate of increase of the circumference of a
circle and that of the area are 3 and 4
respectively, then its radius is​

Answer 1

Answer:

fontsize1810Area is increased by 300 percent.

Step-by-step explanation:

Let r units and r' units denote the radius of the given circle with circumference 4π and 8π respectively.

Then, we have

\begin{gathered}2\pi r=4\pi\\\\\Rightarrow r=\dfrac{4\pi}{2\pi}\\\\\Rightarrow r=2\end{gathered}

2πr=4π

⇒r=

2π

4π

⇒r=2

and

\begin{gathered}2\pi r^\prime=8\pi\\\\\Rightarrow r^\prime=\dfrac{8\pi}{2\pi}\\\\\Rightarrow r^\prime=4\end{gathered}

2πr

′

=8π

⇒r

′

=

2π

8π

⇒r

′

=4

Now, the area of the circle with radius 2 units is

A_1=\pi r^2=\pi \times2^2=4\piA

1

=πr

2

=π×2

2

=4π

and the area of the circle with radius 4 units is

A_2=\pi (r^\prime)^2=\pi \times4^2=16\piA

2

=π(r

′

)

2

=π×4

2

=16π

Therefore, the percent increase in the area of the circle is

\begin{gathered}\dfrac{A_2-A_1}{A_1}\times100\%\\\\\\=\dfrac{16\pi-4\pi}{4\pi}\times100\%\\\\=\dfrac{12\pi}{4\pi}\times100\%\\\\=300\%.\end{gathered}

A

1

A

2

−A

1

×100%

=

4π

16π−4π

×100%

=

4π

12π

×100%

=300%.

Thus, the area of the circle is increased by 300%.

hope it helps

Answer 2

radius is 45 cm longest ok understood