📐 geometry

1. **State the problem:** We have a sector AOB of a circle with an arc length of $8\pi$ cm. When folded, the sector forms a cone. We need to find the radius of the base of this con

1. **Problem Statement:** We have a cylinder inscribed in a sphere of radius $R=3$. We want to find the height $h$ of the cylinder that maximizes its volume.

1. **Problem statement:** We have two gardens sharing a side AB: one is a rectangle (apples) and the other a regular hexagon (roses). The total wire length around both gardens exce

1. **Problem:** Athul walked along the outer edge of a rectangular park with length 30 m and width 23 m. Find the total distance he walked, which is the perimeter of the rectangle.

1. **Problem Statement:** We have two rectangles placed such that the diagonal starts from the right top corner of the first rectangle and ends at the left bottom corner of the sec

1. The problem asks: How many triangles are in the given geometric sketch? 2. The sketch is a large rectangle divided into 3 rows and 3 columns, making 9 smaller rectangles.

1. **Problem statement:** We have a sector DAB of a circle with center A and radius 18 cm.

1. **Zadání problému:** Máme tři útvary: modrý čtverec, žlutý kruh a zelený trojúhelník. Úkolem je vyznačit 6 bodů tak, aby:

1. **State the problem:** Given a circle with radius $OR = 18$ cm and central angle $\angle SOR = 155^\circ$, find:

1. **Problem statement:** We have a sector AOB of a circle with center O and radius 16 cm.

1. The problem is to find the area of a triangle given its base and height. 2. The formula for the area of a triangle is:

1. **State the problem:** Find the area of a circle given its radius. 2. **Formula:** The area $A$ of a circle with radius $r$ is given by the formula:

1. **Stating the problem:** We want to find the side length of a cube that can be inscribed inside a sphere with radius $\frac{3\sqrt{3}}{2}$.\n\n2. **Formula and explanation:** Wh

1. **State the problem:** We have a right triangle ABC with a right angle at C, angle A is 65 degrees, hypotenuse AB is 7 units, and we need to find the length of side AC. 2. **For

1. The problem asks us to identify which shapes among A, B, C, and D are polygons. 2. A polygon is a closed plane figure with straight sides. It must have at least three straight s

1. **Nêu bài toán:** Cho đường tròn $(O; R)$ và điểm $A$ nằm ngoài đường tròn. Từ $A$ vẽ hai tiếp tuyến $AB$ và $AC$ với $B$, $C$ là các tiếp điểm. Đường thẳng $AO$ cắt $BC$ tại $H

1. **Problem Statement:** In a rectangle ABCD, the diagonals AC and BD intersect at O. Given that $\angle BOC = 40^\circ$, find $\angle OBC$ and $\angle OCB$. 2. **Important Proper

1. **Problem a:** Find the measures of the numbered angles in the isosceles trapezoid with one angle given as 66°. 2. **Step 1:** Recall that in an isosceles trapezoid, the base an

1. **State the problem:** Find the area of the polygon with vertices P, Q, R, S, M, N given the side lengths and right angles. 2. **Analyze the shape:** The polygon can be decompos

1. The problem asks: What is length and width? 2. Length and width are terms used to describe the dimensions of a two-dimensional shape, such as a rectangle.

1. **Problem Statement:** Compute the area enclosed by a straight line and a curve given the ordinates at intervals of 7.5 m using the Mid-ordinate rule, Trapezoidal rule, and Simp