14. A right cone has a height of 14 in and a base diameter of 17 in. a Sketch and label a diagram of the cone
b. Determine the area of the lateral surface of the cone, to the nearest square inch​

Given:

The height of a right cone = 14 in

Base diameter = 17 in

To find:

The diagram of the cone and its lateral surface area.

Solution:

(a)

The diagram of a right cone with height 14 in and base diameter of 17 in is shown below.

Diagram is not to scale.

(b)

We know that lateral surface of the cone is

             ...(i)

Where, r is the base radius, h is vertical height and l is the slant height of the cone.

Base radius of the cone =

Now,

Putting r=8.5, h=14 and π=3.14 in (i), we get

Therefore, the lateral surface area of the cone is 437 sq. inches.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

a. -0.3 > -0.33