Question

A pendant is made from two wire circles joined by two straight pieces of wire. The wire circles share the same centre. Work out the integer values that complete the equation below for the total length of wire used in the pendant. 23 mm 57 mm total length of wire = T + mm​

Answer 1

The total length of wire used in the pendant is approximately
`\[ T \approx 144.44 \]`.

The total length of wire used in the pendant, denoted as
`\(T\)`, can be calculated using the formula for the circumference of a circle:

`\[ C = 2\pi r \]`

where
`\(r\)` is the radius of the circle.

In this case, there are two circles, so we need to calculate the total circumference for both circles and add the lengths of the two straight pieces.

1. Circumference of the first circle:

`\[ C_1 = 2\pi r \]`

`\[ C_1 = 2\pi * 23 \]`

2. Circumference of the second circle:

`\[ C_2 = 2\pi r \]`

`\[ C_2 = 2\pi * 23 \]`

3. Length of the straight pieces:

`\[ \text{Length of the straight pieces} = 2l \]`

`\[ \text{Length of the straight pieces} = 2 * 57 \]`

Now, add the lengths of the two circumferences and the length of the straight pieces:

`\[ T = C_1 + C_2 + \text{Length of the straight pieces} \]`

`\[ T = 2\pi * 23 + 2\pi * 23 + 2 * 57 \]`

Now, calculate
`\(T\)` to find the total length of wire used in the pendant.

Let's calculate the total length of wire used in the pendant
`(\(T\))`:

`\[ T = 2\pi * 23 + 2\pi * 23 + 2 * 57 \]`

`\[ T = 46\pi + 114 \]`

Now, since we want the total length in the form
`\(T + \text{mm}\)`, we can use the approximation
`\(\pi \approx 3.14\)` to get an integer value for the total length:

`\[ T \approx 46 * 3.14 + 114 \]`

`\[ T \approx 144.44 \]`

So, the total length of wire used in the pendant is approximately
`\[ T \approx 144.44 \]`.