Question 1 Here is the base of a prism.

a. If the height of the prism is 5 cm, what is its surface area? What is its volume?

b. If the height of the prism is 10 cm, what is its surface area? What is its volume?

c. When the height doubled, what was the percent increase for the surface area? For the volume?

A). Surface area = 222 cm²

Volume = 180 cm³

B). Surface area = 375 cm²

Volume = 360 cm³

C). % increase in surface area = 67.57%

% increase in volume = 100%

Step-by-step explanation:

In the figure attached base of a prism has been given.

A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)

Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8

                                       = 30

Area of the base = 8×5 - 2×2 = 36 cm²

Surface area of the prism = 30×5 + 2×(36)= 222 cm²

Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off

                                  = 8×5×5 - 2×2×5

                                  = 200 - 20

                                  = 180 cm³

B). Surface area of the prism if it's height is 10 cm,

Surface area = 30×10 + 2×(36) = 372 cm²

Volume of the prism = 8×5×10 - 2×2×10

                                   = 400 - 40

                                   = 360 cm³                                      

C). Increase in surface area = 372 - 222 = 150 cm²

% increase in the surface area = = 67.57%

Increase in volume = 360 - 180 = 180 cm³

% increase in volume = = 100%

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 answer is 24

step-by-step explanation: