Answer:
£135 is the correct answer.
Step-by-step explanation:
Let C be the cost of table.
And let R be the radius of table.
Cost of table is directly proportional to square of radius.
As per question statement:
[tex]C\propto R^{2}[/tex] or
[tex]C=a\times R^2 ....... (1)[/tex]
where [tex]a[/tex] is the constant to remove the [tex]\propto sign[/tex].
It is given that
[tex]C_1 =[/tex] £60 and [tex]R_1 = 50\ cm[/tex]
[tex]C_2 = ?[/tex] when [tex]R_2= 75\ cm[/tex]
Putting the values of [tex]C_1[/tex] and [tex]R_1[/tex] in equation (1):
[tex]60=a \times 50^2 ....... (2)[/tex]
Putting the values of [tex]C_2[/tex] and [tex]R_2[/tex] in equation (1):
[tex]C_2=a \times 75^2 ....... (3)[/tex]
Dividing equation (2) by (3):
[tex]\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135[/tex]
So, £135 is the correct answer.
