📐 geometry

1. **State the problem:** We need to find the volume of soup that fits in a cylindrical can with radius $r=3$ cm and height $h=7$ cm. 2. **Formula:** The volume $V$ of a cylinder i

1. **Stating the problem:** We need to calculate the arc length and area of a circle sector with radius $r=16$ m and central angle $\theta=140^\circ$. 2. **Formulas used:**

1. Uzdevums: Ir riņķa līnija ar centru S, uz kuras atzīmēti pieci vienādi loki MN, NK, KL, LR un RM. 2. Mums jāaprēķina trijstūru MNK, MKS un NLR leņķi.

1. **Énoncé du problème :** Calcule le volume d'un cône de hauteur 9 cm et dont le disque de base a un rayon de 4 cm.

1. **State the problem:** We have a triangle with angles $\alpha = 90^\circ$ and $\beta = 40^\circ$. We need to find the third angle $\gamma$. 2. **Formula used:** The sum of the i

1. **Stating the problem:** We need to find the values of angles $h$ and $j$ formed by two intersecting chords inside a circle, given one angle is $39^\circ$ and the other angles a

1. **Stating the problem:** We need to find the values of angles $h$ and $j$ in the given circle diagram where two chords intersect inside the circle. 2. **Relevant formula:** When

1. Given: \(\angle 1\) and \(\angle 2\) form a linear pair, \(\angle 2\) and \(\angle 3\) form a linear pair. 2. Write the equations for the linear pairs:

1. Find the surface area of the rectangular prism with dimensions 20 m, 7 m, and 3.4 m. The formula for the surface area of a rectangular prism is:

1. **Problem Statement:** Find the volume of the given solid, which is a slanted cylindrical solid with a circular top and bottom, where the top diameter is 12 m, the slant height

1. **State the problem:** Find the radius $r$ of a cylinder given its lateral area $18\pi$ and height $h=6$.

1. **Problem:** Find the perimeter and area of a triangle with sides 30 cm, 14.7 cm, and 20 cm, and height 13 cm. 2. **Formulas:**

1. **State the problem:** We are given a skewed rectangular prism-like solid with dimensions 4 ft, 6 ft, 9 ft, and 10 ft, and a volume of 264 ft³. We need to understand how these d

1. **State the problem:** We need to find the area of a quadrilateral with sides 8 ft, 6 ft, 9 ft, and 10 ft, and a diagonal dividing it into two triangles. 2. **Formula used:** Th

1. The problem asks to find the measure of angle $m\angle QS$. 2. To solve this, we need more information about the figure or the relationships between points Q, S, and any other p

1. **Problem:** Find the intercepted arcs and angle measures for points on the circle with points R, Q, S, T and center P. 2. **Formula and rules:**

1. **State the problem:** We are given three parallel lines PA, HK, and BR with points P, A on PA; H, K on HK; and B, Q, C, R on BR. We need to prove that $$|AH| \times |QB| = |AP|

1. **State the problem:** Calculate the surface area of a triangular prism with given side lengths. 2. **Identify the dimensions:** The triangular prism has a triangular base with

1. The problem asks whether skew lines are lines that are not parallel but lie in parallel planes. 2. Skew lines are defined as lines that do not intersect and are not parallel.

1. **Stating the problem:** We have a triangle with an exterior angle measuring 141° and an adjacent interior angle labeled $x^\circ$. The triangle has a right angle at the top ver

1. **Problem statement:** Given the prism ABCDEFGH with points A(6|0|0), B(6|7|0), C(0|7|0), D(0|0|0), E(4|2|5), F(4|9|5), G(-2|9|5), and H unknown.