Question

Let f be the function that determines the area of a circle (in square cm) given the radius of the circle in cm, r. That is, f(r) represents the area of a circle (in square cm) whose radius is r cm. Use function notation to complete the following tasks a. Represent the area (in square cm) of a circle whose radius is 4 cm. Preview syntax error b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm. # Preview syntax error c. Represent the area of 5 circles that all have a radius of 12.7 cm *Preview syntax error d. A circle has a radius of 28 cm. Another larger circle has an area that is 59 square cm more than the first circle. Represent the area of the larger circle. # Preview) syntax error

Answer 1

Answer:

The answers to each question are:

a)$A=f(r=4cm)=50.26cm^2$

b)$\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2$

c)$C=5\cdot f(r=12.7cm)=2533.54cm^2$

d)$D=f(r=28cm)+59cm^2=2522.01cm^2$

Step-by-step explanation:

The function f(r) that represents the area of a circle (in square cm) is:

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

a) To represent the area (in square cm) of a circle whose radius is 4 cm, you just have to evaluate the function with a radius of 4cm:

$A=f(r=4cm)=50.26cm^2$

b) To represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm, you have to represent the difference between the final area with a radius of 10.91cm and the initial area of a radius of 10.9cm:

$\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2$

c) To represent the area of 5 circles that all have a radius of 12.7 cm, we can use the function f(r) to represent the area of a circle with a radius of 12.7cm and multiply it for 5:

$C=5\cdot f(r=12.7cm)=2533.54cm^2$

d) To represent the area of the larger circle that is 59 square cm more than the first circle (with a radius of 28 cm), we can use the function f(r) to obtain the area of the first circle and addition 59 square cm:

$D=f(r=28cm)+59cm^2=2522.01cm^2$