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SSAT Elementary Level
Quantitative (Math)

Comparing Circumference to Perimeter

Hard Geometry And Spatial Sense Shapes

Emily has a collection of different geometric shapes: triangles, squares, and circles. She places these shapes into separate boxes based on their types. Each triangle has 3 sides, each square has 4 equal sides, and each circle does not have any sides. Emily randomly selects one shape from each box and measures their perimeters. The perimeter of a triangle is calculated by adding the lengths of its three sides. The formula for the perimeter of a square is given by $$P = 4s$$, where $$s$$ is the length of a side. The circle’s perimeter is also known as its circumference, which is calculated using the formula $$C = 2\pi r$$, where $$r$$ is the radius of the circle.

After measuring, Emily finds that the triangle has a perimeter of 12 units, the square has a perimeter of 16 units, and the circle has a radius of 3 units. How does the circumference of the circle compare to the total perimeter of the other two shapes combined?

Hint

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