📐 geometry

1. **Stating the problem:** We are given two triangles with angles expressed in terms of $y$ and need to find the value of $y$. 2. **First triangle:** Angles are $y^\circ$, $3y^\ci

1. Problem statement: Find the measure of $\angle CAD$ in terms of $\angle 1$ and $\angle 2$ given that $\overline{BE}$ is parallel to $\overline{FH}$ and $\overline{AG}$ is a stra

1. **State the problem:** We are given the angle measure equation for question 37: $$m\angle 2 = 5x - 8$$ and the angle measure is $$58^\circ$$.

1. **State the problem:** We need to find the exact volumes of a cylinder and a cone, both with radius $r=7$ mm and height $h=6$ mm.

1. **State the problem:** We need to find the radius $r$ of a cone given its height $h=12$ cm and volume $V=36\pi$ cubic cm. 2. **Formula for the volume of a cone:**

1. **State the problem:** We are given a cylinder with volume $178\pi$ cubic inches. We need to find the exact volume of a cone that has the same base area and height as this cylin

1. **State the problem:** We need to find the volume of a cylinder with radius $r = 5.3$ inches and height $h = 8.4$ inches. 2. **Formula for volume of a cylinder:**

1. **State the problem:** Find the exact volume of a cylinder with radius $r=4$ inches and height $h=8$ inches. 2. **Formula:** The volume $V$ of a cylinder is given by the formula

1. **State the problem:** We need to find the volume of a cylinder with radius $r = 5.7$ inches and height $h = 4$ inches. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We need to find the measures of the missing angles $x$ and $y$ given that $x=146^\circ$ and $y=90^\circ$ and one angle is $34^\circ$. 2. **Analyze the giv

1. **State the problem:** We need to find the measures of the missing angles $x$ and $y$ given that one angle is $34^\circ$, $x = 146^\circ$, and $y = 90^\circ$. 2. **Analyze the g

1. **State the problem:** We have two triangles STS and VUW with ST \parallel UW, and we need to find the value of $p$ given the side lengths: $UT=24$, $VU=26$, $VW=16p-3$, and $WS

1. Problemet: Vi ska beräkna den totala begränsningsytan av en cylindrisk burk med höjd $12$ cm och radie $3$ cm. 2. Formler: Den totala ytan av en cylinder består av mantelytan pl

1. **Problem statement:** We need to calculate the lateral surface area (mantelyta) of a cylindrical energy drink can with height $h=12$ cm and radius $r=3$ cm. 2. **Formula:** The

1. The problem is to calculate the area $A$ of a circle using the formula $A = \pi r^2$ and then multiply the result by 12. 2. The formula for the area of a circle is:

1. **State the problem:** We need to find the value of $v$ in parallelogram CDEF where side $CD = 2v$ and the opposite side $EF = v + 19$. 2. **Recall the property of parallelogram

1. **Problem Statement:** Find the value of $x$ in rhombus $RSTU$ where the angle at vertex $R$ is $(x + 18)^\circ$ and the angle at vertex $S$ is $2x^\circ$.

1. The problem asks to find the coordinates of points A' and B' after a dilation of line segment AB with scale factor $\frac{1}{3}$ centered at the origin. 2. The formula for dilat

1. The problem asks to find the coordinates of points A' and B' after a dilation of the line segment AB with a scale factor of 2, centered at the origin. 2. The original points are

1. **State the problem:** We have an isosceles triangle with a base length of 24 cm and total area 220 cm². The triangle is divided into four smaller sections by three lines parall

1. **State the problem:** We need to find the tangent of angle $S$ in a right triangle $TSR$ where the right angle is at $T$. 2. **Recall the definition of tangent:** For an angle