Mathematics: The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs £60. What is the cost of a circular table with a radius of 75cm? Show all your working

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The cost of a circular table is directly proportional

Ответ:

fatherbamboo

29.01.2022

Mathematics

£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:

$C\propto R^{2}$ or

$C=a\times R^2 ....... (1)$

where is the constant to remove the $\propto sign$ .

It is given that

C_1 = £60 and $R_1 = 50\ cm$

C_2 = ? when $R_2= 75\ cm$

Putting the values of C_1 and R_1 in equation (1):

$60=a \times 50^2 ....... (2)$

Putting the values of C_2 and R_2 in equation (1):

$C_2=a \times 75^2 ....... (3)$

Dividing equation (2) by (3):

$\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135$

So, £135 is the correct answer.

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The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs £60. What is the cost of a circular table with a radius of 75cm? Show all your working

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