10) Face diagonal
What is the volume of a cube that has a face diagonal of 5 cm? (to the nearest whole number)
A)
(cm3
B)
18 cm3
25 cm3
D)
43 cm3

the volume of the cube will be 44 cm³ or D (nearest whole number)

Step-by-step explanation:

A cube has equal size of edges. Since it has a face diagonal of 5cm then using Pythagoras theorem s²+ s²= 5², where s is the side of the cube.

Therefore, 2s²=25

                   s²= 12.5

                    s = √12.5 = 3.536 cm

The volume of a cube is s³ (s×s×s) = 3.536³= 44.212 cm³,

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 ☺