📐 geometry

1. The problem asks to solve the volume formula of a cone for the height $h$. 2. The volume formula of a cone is given by:

1. **Problem Statement:** Given triangle ABC with AB = AC and angle BAC = 26°, find the base angles and the exterior angle at vertex B. 2. **Formula and Rules:** In an isosceles tr

1. **Stating the problem:** We are given the mantle area (lateral surface area) of a cylinder as 622 cm\textsuperscript{2} and the radius as 9 cm. We need to find the height of the

1. **Stating the problem:** We have a triangle with one angle of 30° at the bottom-left corner, and two sides adjacent to this angle measuring 10 and 6 units respectively. We want

1. The problem asks to find the volume (rumfanget) of various solids given their height $h$ and base area $G$. 2. The formula for the volume depends on the type of solid:

1. **Problem 1:** Given an isosceles trapezoid ABCD with an inscribed circle of radius 6 and the difference of the bases $AD - BC = 9$, find the perimeter of ABCD. 2. **Formula and

1. **State the problem:** We are given a triangle with three angles labeled as $x^\circ$, $2x^\circ$, and $(x - 20)^\circ$. We need to write an equation modeling the sum of these a

1. **Problem statement:** Calculate the length of the segment $PM$ in the given 3D prism with a trapezoidal base, where $M$ is the midpoint of rectangle $ABCD$. 2. **Understanding

1. **Problem 1:** Given triangle ABC with angles $A=35^\circ$, $B=88^\circ$, and side $AC=44$ mm, find the missing angle $C$ and the missing sides. 2. **Step 1: Find angle $C$ usin

1. **Problem Statement:** Find the lengths of the other two sides of the triangular dog house given the sides are in the ratio 3:3:2 and the shortest side measures 1 meter.

1. **State the problem:** We need to find the area of the sidewalk surrounding a circular pool with diameter 10 meters and sidewalk width 1 meter.

1. **State the problem:** A wheel with diameter 60 cm is rolled 5 times along a straight path. We need to find the distance travelled by the wheel and the degrees the pin rotates a

1. **Problem statement:** Given a figure with segments (AB) parallel to (CD) and (EF), angles BAC = 50° and CFE = ESC, find the measures of angles DCF and CFE.

1. **State the problem:** Find the area of a rectangular room with length 30 feet and width 18 feet. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. 問題: 練習3の(1)点A(1, -1)とB(4, 3)の距離を求めよ。 2. 距離の公式は2点間の距離$d$を

1. **Problem statement:** Four lines intersect at point A forming several angles. Given angles are $4x^\circ$, $(2x+18)^\circ$, and $2x^\circ$. The vertical and horizontal lines ar

1. **Problem statement:** Given that \(\angle FEB\) and \(\angle CFD\) are straight angles (each 180°), and \(\angle EFC\) is a right angle (90°), find the measure of \(\angle CFB\

1. **Problem statement:** We are given that \(\angle AFB\) and \(\angle CFD\) are straight angles, and \(\angle EFC\) is a right angle. We need to find the measure of \(\angle CFB\

1. **Problem statement:** Berechne den Umfang $u$ und den Flächeninhalt $A$ der zusammengesetzten Figur mit $a=8$ cm. 2. **Formeln und Regeln:**

1. **State the problem:** We have a sector OAB of a circle with radius $20$ cm and central angle $\theta$ radians. The perimeter of the sector is $65$ cm. Lines CA and CB are tange

1. **State the problem:** Given that $m\angle SQT = 30^\circ$ and $m\angle P = 85^\circ$, and that $\angle SQT$ and $\angle PQR$ are vertical angles, find $m\angle R$. 2. **Use the