3. The diagram shows a hula hoop with diameter 96.52 cm . Nely spins the hoop for 4 complete rotations. Calculate the distance travelled by the hoop, in metres.

To calculate the distance traveled by the hoop, we need to find the circumference of the hoop and then multiply it by the number of rotations. Given: - Diameter of the hoop = 96.52 cm - Number of rotations = 4 First, we need to find the circumference of the hoop using the formula: \[ \text{Circumference} = \pi \times \text{Diameter} \] Substitute the given diameter into the formula: \[ \text{Circumference} = \pi \times 96.52 \] Next, we need to convert the circumference from centimeters to meters by dividing by 100 (since 1 meter = 100 centimeters). Finally, we multiply the circumference by the number of rotations to find the total distance traveled by the hoop. Let's calculate this step by step. Calculate the value by following steps: - step0: Calculate: \(\pi \times 96.52\) - step1: Simplify: \(96.52\pi \) - step2: Simplify: \(303.226523\) The circumference of the hoop is approximately 303.23 cm. Now, let's convert this to meters by dividing by 100. Calculate the value by following steps: - step0: Calculate: \(\frac{303.226523}{100}\) - step1: Convert the expressions: \(\frac{\frac{303226523}{1000000}}{100}\) - step2: Multiply by the reciprocal: \(\frac{303226523}{1000000}\times \frac{1}{100}\) - step3: Multiply the fractions: \(\frac{303226523}{1000000\times 100}\) - step4: Multiply: \(\frac{303226523}{100000000}\) The circumference of the hoop is approximately 3.032 meters. Now, we need to calculate the total distance traveled by the hoop by multiplying the circumference by the number of rotations (4 rotations). Calculate the value by following steps: - step0: Calculate: \(3.03226523\times 4\) - step1: Multiply the numbers: \(12.12906092\) The distance traveled by the hoop is approximately 12.129 meters.