A printer designs a tag in the shape of circle with a smaller circle cut out. She cuts her prototype from a 6 in. by 8 in. piece of cardstock. The cut edges of the tag will be printed with gold leaf. What is the approximate amount of gold leaf on a tag? The circumference of the larger circle is about inches. The circumference of the smaller circle is about inches. So, the total length of gold leaf on a tag is approximately inches.

The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.

Explanation:

From looking at the picture provided, we can see that the tag is about half of 8. This would mean that the diameter of the larger circle is about 4 inches. To find the circumference of a circle, we would need to know our radius. Half of 4 is 2, so filling in what we know: 2π2 ≈ 4π ≈ 12.56637.

Next, looking at the smaller circle, we can see that its almost about half of the larger circle's radius. We can conclude that the smaller circle would have a diameter of 1 inch. This would mean that its radius is 0.5 inch. So, filling in what we know: 2π0.5 ≈ π ≈ 3.14159.

Looking back at the two problems we've worked out, we know that the circumference of the larger circle is about 12.57 inches and the smaller circle's circumference is about 3.14 inches. So adding both 12.57 and 3.14 will help us find the total length of gold leaf on the tag, which is about 15.71 inches.

- 2022 Edmentum