Question

Three concentric circles are designed as part of a target practice board. Their diameters form an arithmetic progression. If the smallest circle has a circumference of 6∏ cm and the largest circle has a circumference of 14∏ cm. what is the circumference of the middle circle?

• A. 8∏ cm
• B. 10∏ cm
• C. 12∏ cm
• D. 11∏ cm

Answer 1

Answer:

B. 10∏ cm

Circumference (C = \pi d).

Smallest circle:
$6\pi = \pi d_1 \Rightarrow d_1 = 6$

Largest circle:
$14\pi = \pi d_3 \Rightarrow d_3 = 14$

The diameters form an arithmetic progression, so the middle term is the average:
$d_2 = \frac{6 + 14}{2} = 10$

Now find the middle circumference:
$C_2 = \pi d_2 = 10\pi$

Answer: $(\boxed{10\pi \text{ cm}})$