Geometry

Using the distance formula, the horizontal change is 3 - (-1) = 4 and the vertical change is 1 - (-2) = 3. This forms a classic 3-4-5 right triangle, making the straight-line distance 5. Simply adding the absolute differences of the coordinates to get 7 is incorrect because it ignores the Pythagorean theorem.

A circle inscribed in a square has a diameter equal to the square's side length of 10, which means its radius is 5. Using the area formula, the area is pi times 5 squared, which equals 25pi. Choice C is incorrect because it mistakenly uses the side length as the radius, yielding an area of 100pi.

To find the radius, we substitute the given values into the volume formula: 96\pi = \pi r^2 \cdot 6. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !A common error is mistakenly taking half of 16 instead of its square root, leading to an incorrect radius of 8. This confusion arises from not properly applying the formula or misunderstanding the relationship between the volume, height, and radius of a cylinder.
• !A common mistake is selecting 8, which incorrectly divides 16 by 2 instead of taking its square root.
• !Choice C is incorrect because it mistakenly uses the side length as the radius, yielding an area of 100pi.
• !Simply adding the absolute differences of the coordinates to get 7 is incorrect because it ignores the Pythagorean theorem.

Answer each from memory — you'll see instantly whether you're right and why.

Run a focused 10-question mini-mock on Geometry and see it stick.