📐 geometry

1. **State the problem:** We have a right circular cylinder full of ice cream with diameter 12 cm and height 15 cm. We want to find how many cones (each with a hemispherical top) o

1. **Problem statement:** Given triangle ABC with D midpoint of BC, E midpoint of AC, and M the intersection of AD and BE. Given lengths: $AD=6$ cm, $AB=9$ cm, $BE=9$ cm. Find the

1. **Problem statement:** We are given two disks with areas 2.5 and 100, and we want to find the ratio of their radii. 2. **Formula used:** The area $A$ of a disk is related to its

1. **Problem Statement:** Find the Lateral Surface Area (LSA) and Total Surface Area (TSA) of a triangular pyramid with base side length $8\sqrt{3}$ cm. 2. **Understanding the prob

1. **State the problem:** We need to find the total surface area of a triangular prism given its net with dimensions. 2. **Identify the shapes and dimensions:** The net consists of

1. **State the problem:** Calculate the volume of a cylinder with radius $r=4$ cm and height $h=12$ cm, giving the answer to 1 decimal place. 2. **Formula:** The volume $V$ of a cy

1. **Problem statement:** We need to find the coordinates of vertex C' after enlarging triangle ABC with center at (1, 9) and scale factor $\frac{1}{2}$. The original vertex C is a

1. **Stating the problem:** We need to find the measure of angle $\angle AOC$ given the described geometric setup. 2. **Understanding the setup:** Line $AB$ is horizontal with $O$

1. **State the problem:** We are given that line segment \(\overline{AB}\) is congruent to line segment \(\overline{CD}\), meaning their lengths are equal. We need to find the valu

1. **State the problem:** We are given a line segment AB with length 24 units, and point O is the midpoint of AB. We need to find the length of segment BO. 2. **Recall the midpoint

1. The problem states that \(\overline{MT} \cong \overline{KD}\), meaning the lengths of segments MT and KD are equal. 2. Given \(MT = x + 7\) cm and \(KD = 14\) cm, set the expres

1. **State the problem:** You need to find how many 20 kg bags of premixed concrete are required to lay a concrete border around a circular pond.

1. The problem asks which segment is congruent to the given segment of length 18 cm. 2. Congruent segments have the same length.

1. **State the problem:** We have a right triangle NSB with a right angle at N. Segment NW is perpendicular to the hypotenuse BS. Given NB = 12 units and WS = 16.1 units, we need t

1. **State the problem:** We have a right triangle NSB with a right angle at N. Segment NW is perpendicular to the hypotenuse BS, creating two smaller right triangles. We know NB =

1. The problem asks to identify which illustration shows congruent segments. 2. Congruent segments are line segments that have the same length.

1. **Problem:** Find the unknown side length $c$ of a right triangle with legs $a=2$ and $b=3$. 2. **Formula:** Use the Pythagorean theorem: $$c^2 = a^2 + b^2$$

1. Задача: Найти площади фигур, ограниченных кривыми в полярных координатах $R=\frac{5}{2}\sin\varphi$ и $r=\frac{3}{2}\sin\varphi$. 2. Формула для площади фигуры, ограниченной пол

1. **Problem statement:** We are given two similar bars with lengths 57.23 m and 33.2 m. We need to find the maximum possible difference in length between these two bars. 2. **Unde

1. **Problem statement:** We are given two similar bars with lengths 57.23 m and 33.2 m. We need to find the maximum possible difference in length between the two bars. 2. **Unders

1. The problem asks to find the missing side length $x$ using proportions or a table. 2. Given the pairs: $\frac{17.5}{4}$, $\frac{12}{25}$, $\frac{7}{30}$, and $\frac{10}{x}$, we