# The volume V of a growing spherical cell is V = 4 3 πr3, where the radius is measured in micrometers (1 µm = 10−6m). Find the average rate of change of V with respect to r when r changes from 6 to each of the following. (Round your answers to one decimal place.) (i) 6 to 9 µm(ii) 5 to 6 µm (iii) 5 to 5.1 µm

The average rate of volume change of a growing spherical cell for different changes in radius can be calculated using the formula for the volume of a sphere and the formula for average rate of change (ΔV/Δr).

### Explanation:

To find the average rate of change of the volume V with respect to the radius r, you will need to subtract the initial volume from the final volume and then divide by the change in radius. This is represented by the formula ΔV/Δr, where Δ represents change in.

1. For r changing from 6 to 9 µm, ΔV = V(9) - V(6) = 4/3π(9^3) - 4/3π(6^3). Therefore, ΔV/Δr = (4/3π(9^3) - 4/3π(6^3)) / (9 - 6).
2. For r changing from 5 to 6 µm, ΔV = V(6) - V(5) = 4/3π(6^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(6^3) - 4/3π(5^3)) / (6 - 5).
3. For r changing from 5 to 5.1 µm, ΔV = V(5.1) - V(5) = 4/3π(5.1^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(5.1^3) - 4/3π(5^3)) / (5.1 - 5).

These calculations will give you the average rate of volume change for each of the radius changes indicated.

brainly.com/question/31995840

#SPJ3

## Related Questions

the cube of the sum of 4 and 9 times x divided by the product of 5 times x and the difference of x and 1​

Step-by-step explanation:

(4 + 9x)^3 represents "the cube of the sum of 4 and 9 times x"

and if we divide by "the product of 5 times x and the difference of x and 1," we get

(4 + 9x)^3

-----------------------

5x(x - 1)

What exactly do you need to know, or to do?

Driscoll Middle School held basketball tryouts after school. Out of the 80 students, only 25% made the team. How many students made it on the team?

A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?

8.3%

Step-by-step explanation:

C) Which of these numbers is a square number?
A B C D
4х 10 9x 10* 4x 10 9x 10​

Mark's football team has scored about 24 points each game. They played 12 games this season.What is the best estimate for the total number of points they scored in the season?

36

Step-by-step explanation:

well you could add 24+12 which equals 36

a rectangular parking lot has length that is greater than the width the area of the parking lot is 160 square yards find the length and the width use formula area=length*width the parking lot length

let 'w' represent the width of the parking lot, then 'w+6' represents its length

area = width * length

160 = w * (w+6)

solving for 'w' we have a positive value of w=10

10+6=16

the width of the parking lot is 10 yards, the length of the parking lot is 16 yards

To find the length and width of a rectangular parking lot given its area, we can use the formula Area = Length * Width. We can set up an equation using this formula and solve for the length and width by factoring or using the quadratic formula.

### Explanation:

To find the length and width of the rectangular parking lot, we can use the formula for the area of a rectangle: Area = Length * Width. We are given that the area is 160 square yards. Let's assume the width of the parking lot is x yards. Since the length is greater than the width, we can say that the length is x + k yards, where k is some positive value.

Substituting the values into the formula, we get:
160 = (x + k) * x

To solve for x, we can rearrange the equation into a quadratic equation:
x^2 + kx - 160 = 0

This equation can be factored or solved using the quadratic formula to find the values of x and k, which represent the width and length of the parking lot, respectively.