Question

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

Answer 1

The cost of a circular table with a radius of 75cm, when the cost is directly proportional to the square of the radius, would be £90. This is found using the ratio of the squares of the radii and the known cost of a smaller table.

Step-by-step explanation:

The cost of a circular table is directly proportional to the square of the radius. This means that if we know the cost and radius of one table, we can calculate the cost of another table by using the ratio of the squares of their radii.

Let's denote the cost of the first table as C1 and the radius as r1, and similarly the cost of the second table as C2 and the radius as r2. The relationship between the costs and radii is:

C1 / C2 = (r1 / r2)^2

We know that C1 is £60 and r1 is 50cm for the first table. We want to find C2 for the table with r2 being 75cm.

£60 / C2 = (50cm / 75cm)^2

Calculating the ratio of the radii squared:

(50cm / 75cm)^2 = (2/3)^2 = 4/9

Therefore:

£60 / C2 = 4/9

Multiplying both sides by C2 and then by 9/4 gives:

C2 = £60 * (9/4)

C2 = £90

So, a circular table with a radius of 75cm would cost £90.

Answer 2

£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* R^2 ....... (1)`

where
`a` 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 * 50^2 ....... (2)`

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

`C_2=a * 75^2 ....... (3)`

Dividing equation (2) by (3):

`(60)/(C_2)= (a * 50^2)/(a * 75^2)\\\Rightarrow (60)/(C_2)= (50^2)/(75^2)\\\Rightarrow (60)/(C_2)= (2^2)/(3^2)\\\Rightarrow (60)/(C_2)= (4)/(9)\\\Rightarrow C_2 = 15 * 9 \\\Rightarrow C_2 = 135`

So, £135 is the correct answer.