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.

replication and blocking

step-by-step explanation:

the answer is b.

64

step-by-step explanation:

c=2πr=2·π·8≈64

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus