📐 geometry

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

1. **Problem:** Find the value of side AB in a right triangle with vertices A, B, C, where angle B is 90°, AC = 12, and angle C = 62°. 2. **Formula:** Use the sine function in a ri

1. **Problem:** Work out the bearings of P from Q for diagram (a). 2. **Understanding bearings:** Bearings are measured clockwise from the North direction.

1. Το πρόβλημα ζητά να κατανοήσουμε την έννοια της ευθείας στη μαθηματική ενότητα της ευθείας. 2. Μια ευθεία είναι το απλούστερο γεωμετρικό αντικείμενο που εκτείνεται απεριόριστα π

1. **State the problem:** We are given two intersecting lines forming four angles labeled 1, 2, 3, and 4. We know that $m\angle 2 = 126^\circ$. We need to find $m\angle 1$, $m\angl

1. **State the problem:** We need to find the size of angle $x$ in triangle $BEG$ given that lines $ABC$ and $DEF$ are parallel and several angles are provided. 2. **Identify known

1. **State the problem:** Macsen's garden has a right triangle with base 14 m and height 16 m, and an inscribed circle with diameter 7 m. We need to find how many bags of gravel ar

1. **State the problem:** Find the perimeter of a composite figure made of a rectangle and a semicircle attached on one side. 2. **Given dimensions:** Rectangle height = 6 m, width

1. The problem states that a map is drawn to a scale of 1 cm to 10 km. 2. We need to express this scale in the form 1 : n, where both units are the same.