One-quarter of a circular pizza of radius 21 cm was removed from the whole pizza. What is the perimeter (in cm) of the remaining pizza?

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Accepted Answer

Step 1: Calculate the circumference of the whole pizza.
Circumference = 2 * π * radius = 2 * 22/7 * 21 = 132 cm.

Step 2: Since one-quarter of the pizza is removed, the remaining pizza is three-quarters of the circle.
The curved edge length of the remaining pizza = (3/4) * 132 = 99 cm.

Step 3: The removed quarter creates two straight edges along the radius lines.
Each radius is 21 cm, so total length of the two straight edges = 2 * 21 = 42 cm.

Step 4: The perimeter of the remaining pizza is the sum of the curved edge and the two straight edges:
Perimeter = 99 + 42 = 141 cm.

Step 5: But the question asks for the perimeter of the remaining pizza, which includes the curved edge plus the two straight edges.

Rechecking calculations:
Curved edge length = (3/4) * 2 * π * 21 = (3/4) * 132 = 99 cm
Straight edges = 2 * 21 = 42 cm
Total perimeter = 99 + 42 = 141 cm

Therefore, the correct perimeter is 141 cm.

Note: The options given are 99, 141, 128, 131. The correct answer is 141.

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