Final answer:
The perimeter of a semicircle with a radius of 3cm is calculated by adding the curved edge, which is half the circumference of a full circle (πr), to the diameter (2r). Hence, the perimeter P is P = 3π + 6cm, given in terms of pi.
Step-by-step explanation:
Calculating the Perimeter of a Semicircle
To calculate the perimeter of a semicircle with a radius of 3cm, you first need to understand that the perimeter P of a full circle is given by the formula P = 2πr, where π represents the constant pi and r is the radius. Since a semicircle is half of a circle, its curved edge will have half the perimeter of a full circle, which is πr. However, the perimeter of a semicircle also includes the diameter (which is the straight line across the semicircle), hence you add 2r (the diameter) to πr (half the circumference). Therefore, the perimeter of a semicircle P is given by P = πr + 2r.
Substituting the given radius (3cm) into the formula, we get P = π × 3cm + 2 × 3cm. To give the answer in terms of pi, the calculation will be P = 3π + 6.
Finally, the perimeter of the semicircle is given by P = 3π + 6cm.