Question

The function f(r) = π determines the area of a circle in cm2, A, in terms of the radius of the circle in cm, r. a. Write a function g that determines the radius of a circle in cm, r, in terms of the area of the cirlce in cm2,A. 9(A)t Preview syntax error b. Use function notation to answer the following questions: i. What is the area (in cm2) of a circle whose radius is 2.58 cm? Preview ii, What is the radius (in cm) of a circle whose area is 1530 cm? *Preview iii. How much greater is the area of a circle whose radius is 15.2 cm than the area of a circle whose radius is 15.1 cm?

Answer 1

Answer with Step-by-step explanation:

We are given that

a.$f(r)=\pi r^2$

$A=\pi r^2$

$r^2=\frac{A}{\pi}$

$g(A)=r=\sqrt{\frac{A}{\pi}}$

b.Radius=2.58 cm

Substitute the values in the formula and $\pi=3.14$

$f(2.58)=3.14(2.58)^2=20.9 cm^2$

Hence, the area of circle =20.9 square cm

c.Area of circle=1530 square cm

$r=\sqrt{\frac{1530}{3.14}}=22.07 cm$

Hence, the radius of circle=22.07 cm

c.Area of circle of radius 15.2 cm=$A_1=3.14(15.2)^2=725.47 cm^2$

Area of circle of radius 15.1 cm=$A_2=3.14(15.1)^2=715.95 cm^2$

$A_1-A_2=725.47-715.95=9.52 cm^2$

Hence, the area of circle whose radius is 15.2 cm is greater than the area of circle of radius 15.1 cm by 9.52 square cm .