📐 geometry

1. **Problem 8: Find the volume of a right circular cylinder with diameter 8 cm and height 18 cm.** 2. The formula for the volume of a cylinder is $$V = \pi r^2 h$$ where $r$ is th

1. **Problem 1: Find the area of a trapezoid** with height $7.5$ ft and bases $7.5$ ft and $15$ ft. 2. The formula for the area of a trapezoid is:

1. **Problem statement:** We need to find the total surface area of a trapezoidal prism box including the flaps. The flaps area is given as 84 cm². 2. **Given dimensions:**

1. **Problem statement:** We have triangle ABC with point D on side AC such that segment BD bisects angle ABC. Given AB = 19, AD = 14, DC = 17, and BC = x, we need to find the valu

1. **State the problem:** A Ferris wheel has a diameter of 140 feet and 40 cars placed evenly around it. We need to find the distance between adjacent cars. 2. **Formula used:** Th

1. **Problem statement:** Given triangle ABC with segment BD bisecting angle ABC, sides AB = 18, BC = 19, AD = x, and DC = 11. We need to find the value of $x$. 2. **Formula used:*

1. **State the problem:** We need to find the exact surface area of a cylinder given its net.

1. **State the problem:** We are given a parallelogram with sides and angles labeled, and we need to find the values of $x$, $m\angle ADB$, and $m\angle A$. 2. **Use properties of

1. **State the problem:** We need to find the area of a semi-circular field with a diameter of 18 meters. 2. **Formula for the area of a circle:** The area $A$ of a full circle is

1. **State the problem:** Calculate the surface area of a rectangular prism with dimensions 4 cm (height), 3 cm (width), and 50 mm (length). 2. **Convert all dimensions to the same

1. **State the problem:** Calculate the surface area (SA) of a rectangular prism with dimensions 5 cm (height), 4 cm (width), and 80 mm (length). 2. **Convert all dimensions to the

1. **Problem Statement:** We are given a circle with points H, I, F, and G on its circumference. The arcs IF and HG measure 84° and 103° respectively. We need to find the measure o

1. **Stating the problem:** We need to find the measure of angle $\angle G$ formed by points $G$, $F$, and $E$ on a circle. 2. **Given information:** The measure of the arc $\overs

1. **State the problem:** We need to find the value of $x$ given that the angle at point $D$ inside the circle is $4x$ and the angle at point $E$ on the circumference is $62^\circ$

1. **State the problem:** We need to find the measure of angle $F$ given two expressions for angles related to points on a circle: $2x - 85^\circ$ and $x - 22^\circ$. 2. **Understa

1. **State the problem:** We need to find the measure of angle $\angle S$ given two expressions for angles related to chords intersecting inside a circle. 2. **Identify the relatio

1. **State the problem:** We need to find the measure of angle RTS in triangle RTS inscribed in a circle. 2. **Given information:**

1. **State the problem:** We have two chords RU and ST intersecting inside a circle, forming angles 13x and 3x + 40° respectively. We need to find the value of $x$. 2. **Formula us

1. **State the problem:** We are given a kite with two numbered angles, $\angle 1 = 18^\circ$ and $\angle 2 = 60^\circ$, and we need to find the measures of these angles. 2. **Reca

1. **State the problem:** We have a pentagon with interior angles labeled as $80^\circ + y^\circ$, $62^\circ$, $95^\circ + x^\circ$, $53^\circ$, and $z^\circ$. We need to find the

1. Tehtävässä on teltan muotoinen kappale, joka koostuu pohjaympyrästä ja kartio-osasta. 2. Annetut tiedot: