Question

At a local park Sara can choose between two circular pathd to wal One path has a diameter of 120 yards and the other has a radius of 45 yards how much farther can sara wal on the longer path than the shorter path if she wals around the path once

Answer 1

Sara can walk π × 30 yards farther on the path with a diameter of 120 yards compared to the path with a radius of 45 yards.

Step-by-step explanation:

To compare the distances Sara can walk on two circular paths, we calculate their circumferences using the formula C = πd, where C is the circumference and d is the diameter. For the path with a diameter of 120 yards, the circumference is C1 = π × 120 yards. The second path has a radius of 45 yards which means the diameter is 90 yards, so the circumference is C2 = π × 90 yards.

Now, let's calculate both circumferences:

• C1 = π × 120 yards
• C2 = π × 90 yards

We can subtract the smaller circumference from the larger one to find how much farther Sara can walk on the longer path:

Distance Difference = C1 - C2

Distance Difference = (π × 120 yards) - (π × 90 yards)

Simplifying, we get:

Distance Difference = π × (120 yards - 90 yards)

Distance Difference = π × 30 yards

So, Sara can walk π × 30 yards farther on the longer path.