Question

A disk has a diameter of 23cm, the inner hole in the disk has a radius of 2 cm. Find the circumference of both the inner hole and the entire disk (rounded to the nearest whole centimeter).

A. Inner hole: 6cm; whole disc: 72cm
B. Inner hole: 13cm; whole disc: 144cm
C. Inner hole: 6cm; whole disc: 144cm
D. Inner hole: 13cm; whole disc: 72cm

Answer 1

Using the circumference formula C = 2πr, the circumferences for the inner hole and the entire disk are found to be 13 cm and 72 cm respectively, making option D the correct answer.

Step-by-step explanation:

To find the circumference of a circle, we use the formula C = 2πr. In the case of the disk with a diameter of 23 cm, the radius (r) is half of that, which is 11.5 cm. Therefore, the circumference of the entire disk is:

C = 2π(11.5 cm)

Approximately, this comes out to:

C ≈ 2(3.1416)(11.5 cm) ≈ 72.256 cm

Since we need to round to the nearest whole centimeter, the entire disk's circumference rounds to:

72 cm

For the inner hole with a radius of 2 cm, its circumference is calculated similarly:

C = 2π(2 cm)

Which approximately equals:

C ≈ 2(3.1416)(2 cm) ≈ 12.57 cm

Rounded to the nearest whole centimeter, the circumference of the inner hole is:

13 cm

Therefore, the correct answer is:

• Inner hole: 13 cm
• Whole disk: 72 cm

This corresponds to option D.