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.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this