(1)を教えて---**Extraction Content:** **Problem Title:** 94 最大値・最小値の図形への応用 (Maximum/Minimum value application to figures) **Question Stem:** 右図のように, 1辺の長さが2a (a>0) の正三角形から, 斜線を引いた四角形をきりとり, 底面が正三角形のフタのない容器を作り, この容積をVとおく。 (As shown in the figure on the right, a container without a lid is made by cutting out the shaded quadrilaterals from an equilateral triangle with side length 2a (a>0), and with the bottom being an equilateral triangle. Let the volume of this container be V.) **Sub-questions:** (1) 容器の底面の正三角形の1辺の長さと容器の高さをxで表せ。 ((1) Express the side length of the equilateral triangle at the bottom of the container and the height of the container in terms of x.) (2) xのとりうる値の範囲を求めよ。 ((2) Find the range of possible values for x.) (3) Vをxで表し, Vの最大値とそのときのxの値を求めよ。 ((3) Express V in terms of x, and find the maximum value of V and the value of x at that time.) **Diagram Description:** * **Type:** Geometric figure illustrating the construction of a container from an equilateral triangle. * **Main Elements:** * **Outer Shape:** A large equilateral triangle. * **Vertices:** The vertices of the outer triangle are not explicitly labeled with letters but are shown. * **Side Length:** One side of the large equilateral triangle is labeled "2a". * **Inner Shape:** An inner equilateral triangle is formed by dashed lines. This represents the base of the container. * **Cut-out Areas:** Three shaded quadrilaterals are located at the corners of the large triangle, outside the inner dashed triangle. These are the areas being cut out. * **Folds:** Three dashed lines connect the vertices of the inner triangle to points on the sides of the outer triangle. These represent fold lines. * **Parameter x:** The length labeled "x" is shown multiple times. It represents the side length of a small triangle (specifically, a right-angled triangle) cut from each corner before forming the quadrilateral. It is also shown as the length along the edge of the large triangle from a vertex to the corner of the shaded quadrilateral. * **Right Angles:** Right angle symbols are indicated at the vertices of the small right-angled triangles near the corners of the large triangle, suggesting that the cuts involve forming right angles from the sides of the large triangle. They are also shown where the sides of the cut-out quadrilaterals meet the dashed fold lines, implying the walls are folded upwards perpendicular to the base. * **Relative Position:** The inner equilateral triangle is concentric with the outer one. The shaded quadrilaterals are at the corners of the outer triangle. **Other Relevant Text:** * **精講 (Hint/Explanation):** 最大値, 最小値の考え方を図形に応用するとき, 変数に範囲がつくことを忘れてはいけません. この設問では (2) です. 考え方は「容器ができるために必要な条件は?」です. (When applying the concept of maximum/minimum values to figures, you must not forget that the variable will have a range. In this question, it is (2). The way of thinking is "What are the necessary conditions for the container to be formed?") * **Page Number:** 149 No options (A, B, C, D) are present in this content.