📐 geometry

1. **State the problem:** Jenny claims the volume of the rectangular prism with dimensions 25 cm (length), 5 cm (height), and 2 cm (width) is 250 cubic centimeters because she calc

1. **State the problem:** Calculate the volume of a pentagonal prism with given edge lengths. 2. **Formula:** The volume $V$ of a prism is given by:

1. **State the problem:** Calculate the volume of a 3D shape that consists of a rectangular base and a triangular prism roof. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the volume of a 3D house-shaped figure composed of a rectangular base and a triangular prism roof. 2. **Identify the shapes and dimensions

1. Problem: Vi skal undersøge, om 10 liter maling kan være i en cylinderformet spand med radius og højde på 15 cm. 2. Formel: Volumen af en cylinder er $$V = \pi r^2 h$$ hvor $r$ e

1. **State the problem:** We need to find the volume of a sphere with diameter 6 units. 2. **Formula for the volume of a sphere:**

1. Problem: Vi skal finde ud af, om 10 liter maling kan være i en cylinderformet spand med radius $r=15$ cm og højde $h=15$ cm. 2. Formel: Volumen af en cylinder er givet ved $$V=\

1. **Problem:** Find the values of $x$ and $y$ in the first triangle where the hypotenuse is 20 and the angle opposite side $y$ is 30°. 2. **Formula and rules:** In a 30°-60°-90° r

1. Problemet handler om at vise, at arealet af et A0-papir er cirka 1 m². 2. Arealet af et rektangel beregnes som længde gange bredde: $$A = l \times b$$

1. Problem: Vis, at arealet af et A0-papir er cirka 1 m². 2. Formlen for arealet af et rektangel er $$A = \text{længde} \times \text{bredde}$$.

1. **State the problem:** We need to find the surface area of a rectangular prism with height $h=87$ and base side length $b=54$. Since only one base side is given, we assume the b

1. **State the problem:** We are given two parallel lines cut by a transversal, forming a triangle with angles labeled $x + 25^\circ$ and $x - 5^\circ$. We need to find the value o

1. **Problem statement:** A piste is 1200 meters long down the mountain with a height difference of 450 meters. We need to find the horizontal distance (a) and the steepness of the

1. **State the problem:** We have an isosceles triangle \(\triangle LMN\) with base \(NL\). The angles are given as \(m \angle N = (2x + 33)^\circ\) and \(m \angle L = (3x + 24)^\c

1. Planteamos el problema: calcular el área de sectores circulares o sectores anulares dados los radios y el ángulo central en grados. 2. Fórmula para el área de un sector circular

1. **State the problem:** Find the area of the polygon with given side lengths and shape. 2. **Analyze the polygon:** The polygon is formed by eight connected line segments with le

1. **State the problem:** We are given a cube with a surface area of 294 cm² and need to find its volume. 2. **Recall the formulas:**

1. **State the problem:** We have a right triangle with one leg of length 11 and hypotenuse of length $x$. We need to find the length of the other leg in simplest radical form with

1. **Problem statement:** We have a right triangle with one leg labeled $x$, the other leg labeled $7$, and the hypotenuse is a side of an equilateral triangle. We need to find $x$

1. **Problem statement:** We have an isosceles right triangle with two equal sides each of length $x$ and the base side length is 1. We need to find the length of side $x$ in simpl

1. **Problem statement:** We have a square with side length $x$ and half of its diagonal labeled as $\sqrt{6}$. We need to find $x$ in simplest radical form with a rational denomin