Find the surface area of the cone with a diameter of 12 centimeters and a slant height of
85 millimeters.
Please answer due in 20 minutes

lateral surface area is 160.14 square cm.

Total surface area is 273.16  square cm  

Step-by-step explanation:

Lateral surface area of cone is given by

where r is radius of cone

and l is slant height of cone.

l = 85 millimetres

we know that 10 millimetres is equal to 1 cm

Thus 85 millimetres is equal to 8.5 cm

Thus slant height(l) in cm is 8.5

we will use value of as 3.14

Diameter of cone = 12 cm

we know that radius is equal to half of Diameter

radius of given cone = 1/2 *Diameter = 1/2 * 12 = 6 cm.

Thus lateral surface area of cone is given by

Thus, lateral surface area is 160.14 square cm.

Area of base of cone will be area of circular base

area of circle is given by

Thus area of base is given below

area of base is 113.04 square cm

Total surface area of cone is sum of area of base and lateral surface area

Total surface area = 160.14+113.04 = 273.16  square cm.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.