Question Video: Application on the Area of the Circles Mathematics • 7th Grade

A pendant is made out of silver. Calculate the area of the face of the pendant.

01:35

Video Transcript

A pendent is made out of silver. Calculate the area of the face of the pendant. And we have a diagram here where the pendant is this shaded portion here.

So this pendant is a large circle and then it has a smaller circle cut out to the middle of it. And itโ€™s that sort of doughnut shape thatโ€™s left that weโ€™re looking to calculate the area of. So we can do this by working out the area of the larger circle and then subtracting the area of the smaller circle. Now the larger circle, if we just think about it, has this radius here and that radius, well, itโ€™s two centimetres plus one centimetre. So this larger circle has a radius of three centimetres. So our area formula is ๐œ‹๐‘Ÿ squared. And weโ€™re gonna be doing the large area subtract the small area. So we just need to substitute in the relevant radii.

So for the larger circle, itโ€™s ๐œ‹ multiplied by three squared and for the smaller circle itโ€™s ๐œ‹ multiplied by two squared. Now if we evaluate each of these, we have nine ๐œ‹ subtract four ๐œ‹. And nine ๐œ‹ subtract four ๐œ‹ is equal to five ๐œ‹. I havenโ€™t been asked to leave my answer in terms of ๐œ‹, so Iโ€™ll evaluate it as a decimal. And using my calculator, this gives an answer of 15.7 centimetres squared to one decimal place. So that gives us the area of this pendant here.

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