Question

the diagram shows 3 identical circles inside a rectangle. each circle touches the other two circles and the sides of the rectangle, as shown in the diagram. the radius of each circle is 32mm. work out the area of the rectangle. give your answer correct to 3 significant figures.

Answer 1

Answer:

2640mm

Step-by-step explanation:

I'm assuming you need the area of the rectangle which the circles don't take up.

First, to find the area of the whole rectangle:

length x width

to find length:

the length is 1 circle, therefore it is the diameter of the circle, which is 32 x 2 = 64mm

to find width:

the width is 3 circles, which is the radius 6 times, so 32 x 6 = 192mm

So, area of rectangle = 64 x 192 = 12288mm

Now to find the area the circles take up:

area of 1 circle =

$\pi \times {r}^{2}$

=

$\pi \times {32}^{2}$

=

$1024\pi$

As we have 3 circles, we multiply this by 3:

$1024\pi \times 3 = 3072\pi$

Finally we subtract the area of the three circles from the area of the rectangle:

$12288mm - 3072\pi = 2637$

As we need to round it to 3 significant figures, the answer is 2640mm