Решение: Calculate the volume of the cylinder, shown on the picture. (The picture shows a cylinder.
Calculate the volume of the cylinder, shown on the picture. (The picture shows a cylinder. A diagonal line from the top edge to the bottom base makes a $ 60^\circ $ angle with the bottom base. The vertical height from the top point of the diagonal to the bottom base is $ 12 $. This height is the cylinder's height.)
Решение по шагам
2 шагаFind the radius of the cylinder base using the right triangle formed by the height, radius, and diagonal. The diagonal makes a 60° angle with the base, so tan(60°) = opposite/adjacent = height / radius. Given height = 12, tan(60°) = √3, so √3 = 12 / r → r = 12 / √3 = 4√3.
$$r = \frac{12}{\sqrt{3}} = 4\sqrt{3}$$Compute the volume of the cylinder using V = πr²h. Substitute r = 4√3 and h = 12: V = π × (4√3)² × 12 = π × (16 × 3) × 12 = π × 48 × 12 = 576π.
$$V = \pi (4\sqrt{3})^2 \cdot 12 = \pi \cdot 48 \cdot 12 = 576\pi$$Где здесь ошибаются
Confusing sine and tangent: using sin(60°) = √3/2 to find radius as 12/(√3/2) = 8√3, leading to V = π(8√3)²·12 = 2304π (not an option).
Forgetting to square the radius: using V = πrh instead of πr²h, giving V = π·4√3·12 = 48√3π (not an option).
Miscalculating (4√3)² as 4·3 = 12 instead of 16·3 = 48, leading to V = π·12·12 = 144π (not an option).