The diameter of a roller is 84 cm and it's length is 120 cm. it takes 500 complete revolutions to move once over to level a playground. find the area of playground in m².

we are given

diameter=84cm

so,

radius =r=42cm

height=h=120cm

we know that

shape of roller is always in cylinder form

now, we can find surface area of cylinder

now, we can plug values

we know that

In one rotation , it covers area is 31667.25395 cm^2

There are 500 rotation

so, total area =

total area =

now, we need to change that area into m^2

we know that

now, we can multiply both sides 15833626.975

we get

so,

Area of playground is .............Answer

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

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step-by-step explanation: