Geometry & Measures

The volume of a cone is V = (1/3)πr²h; substituting r = 3 cm and h = 7 cm gives V = (1/3)·3.14·9·7 ≈ 65.9 cm³, which rounds to about 66 cm³, the value listed in answer B. Answer C (≈88 cm³) comes from omitting the one‑third factor, which inflates the result, and the other choices are either too low or too high relative to the correct calculation.

Since sinθ = opposite/hypotenuse = 3/5, the Pythagorean identity gives cosθ = √(1−sin²θ) = √(1−(3/5)²) = √(1−9/25) = √(16/25) = 4/5, which corresponds to answer B. Option A (3/4) mistakenly swaps the numerator and denominator, ignoring that the hypotenuse remains 5, and the other options exceed 1, violating the range of cosine for real angles.

The interior angle of a regular octagon is 135 degrees, calculated by subtracting the exterior angle of 45 degrees (360 divided by 8) from 180 degrees. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option A is incorrect because 120 degrees is the interior angle of a regular hexagon, which has only six sides.

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