📐 geometry

1. **State the problem:** We have a square with side length 14 cm, and inside it are two quarter circles drawn from opposite corners forming a lens-shaped shaded area. We want to f

1. **State the problem:** Given a triangle with sides $(2x - 1)$ cm, $(x - 1)$ cm, and $(x + 1)$ cm, the largest angle is $120^\circ$. We need to find the value of $x$ and then the

1. We are asked to find the area of a right-angled triangle with side lengths 3 m (height) and 14 m (base). 2. The formula for the area of a right-angled triangle is $$\text{Area}

1. **State the problem:** We are given the volume $V = 2279.64$ cubic feet of a cone and the radius of the base $r = 11$ feet. We need to find the height $h$ of the cone. 2. **Reca

1. **State the problem:** We need to find the volume of a cone with height $h = 19$ yards and radius $r = 8$ yards. 2. **Recall the formula for the volume of a cone:**

1. The problem states that a cone has a height of $19$ yards and a radius of $8$ yards, and we need to find its volume rounded to the nearest hundredth. 2. The formula for the volu

1. **State the problem:** You are given a cone with height $h = 16$ cm and diameter $d = 12$ cm, and you need to find its volume rounded to the nearest hundredth. 2. **Find the rad

1. The problem is to find the volume of a cone with height $h = 19$ mm and radius $r = 17$ mm. 2. The formula for the volume $V$ of a cone is:

1. **State the problem:** Find the volume of a cone with radius $r=8$ mm and height $h=10$ mm. 2. **Recall the formula:** The volume $V$ of a cone is given by

1. **State the problem:** Find the volume of a cone with height $h = 18$ mm and diameter $d = 22$ mm. 2. **Identify the radius:** The radius $r$ is half of the diameter, so $$r = \

1. **State the problem:** We are given a cone with height $h = 8$ cm and radius $r = 7$ cm, and we need to find its volume. 2. **Recall the formula for the volume of a cone:** The

1. The problem asks for the volume of a cone with a height of $20$ yards and a radius of $18$ yards. 2. The formula for the volume $V$ of a cone is $$ V = \frac{1}{3} \pi r^2 h $$

1. The problem requires finding the volume of a cone with a height of $8$ mm and radius of $8$ mm. 2. Recall the formula for the volume of a cone:

1. The problem asks to find the volume of a cone with height $h=12$ yd and radius $r=8$ yd. 2. The formula for the volume of a cone is $$V=\frac{1}{3}\pi r^2 h$$

1. **Problem Statement:** We will review major surface area and volume formulas of common 3D shapes and the concepts behind them. 2. **Surface Area Concept:** Surface area is the t

1. The problem is to find the surface area of a given three-dimensional object. 2. To proceed, we need the exact shape and its dimensions (e.g., sphere radius $r$, cylinder radius

1. **Problem Statement:** We have a triangle with vertices A(-2,-1), B(2,-1), and C(2,2). We need to answer several questions about its perimeter, angles, areas, lines, special poi

1. Problem 33: Describe the opposite angles of a quadrilateral inscribed in a circle. In a cyclic quadrilateral (one inscribed in a circle), the sum of each pair of opposite angles

1. Problem 20: Which of the following angles is formed when an inscribed angle intercepts a semicircle? When an inscribed angle intercepts a semicircle, it always forms a right ang

1. \textbf{نص المشكلة:} لدينا متوازي أضلاع $ABCD$ مع نقطة $N$ حيث $\overrightarrow{AN} = 3 \overrightarrow{AD}$ ونقطة $M$ حيث $\overrightarrow{BM} = \frac{1}{2} \overrightarrow{AB}

1. The problem asks to identify the type of angle for the equation $y = 80^6$. 2. The value $80^6$ represents an angle measure in degrees.