The distance covered by the merry-go-round when it rotates through an angle of 72° is equal to the arc length of the corresponding sector of the circle with radius 10 ft and central angle 72°.
The formula for arc length is:
Arc length = (central angle / 360°) x 2πr
where r is the radius of the circle.
Substituting the given values, we get:
Arc length = (72° / 360°) x 2π(10 ft)
= 0.2 x 20π
= 4π ft
≈ 12.6 ft (rounded to the nearest tenth)
Therefore, the distance covered by the merry-go-round is approximately 12.6 feet.