If the radius of a circle be reduced by 50% its area is reduced by:_________?
Correct answer: C. 75%
- A. 25 %
- B. 50%
- C. 75%
- D. 100%
Explanation
Reducing the radius by 50% leaves a radius of 0.5r. The new area is π(0.5r)² = 0.25πr², so 25% remains and the reduction is 100% - 25% = 75%; option b, 50%, incorrectly applies the radius change directly to area.
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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.
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