📐 geometry

1. **State the problem:** We have a cuboid with dimensions 12 cm, 5 cm, and $x$ cm. The volume of the cuboid is given as 240 cm$^3$.

1. **Problem Statement:** We are given the net of a cuboid drawn on millimeter squared paper, where each square in the net has side length 1 mm. We need to determine the volume of

1. **State the problem:** Calculate the volume of a cube with edge length 1 cm. 2. **Formula:** The volume $V$ of a cube with edge length $a$ is given by the formula:

1. **State the problem:** Calculate the volume of a cuboid with dimensions 3 cm, 5 cm, and 7 cm. 2. **Formula:** The volume $V$ of a cuboid is given by the product of its length, w

1. **State the problem:** We need to find the volume of a cuboid with length 10 cm, width 4 cm, and height 7 cm. 2. **Formula:** The volume $V$ of a cuboid is given by the formula:

1. **State the problem:** We need to find the volume of a cuboid made up of small cubes, where the cuboid has dimensions 5 cm in height, 6 cm in width, and 7 cm in depth. 2. **Form

1. **Problem Statement:** We have a triangle EFD with sides EF = 15 cm, FD = 5 cm, and angle EFD = 10 degrees. We want to find the length of side ED. 2. **Formula Used:** We use th

1. **Problem 1:** Find the missing angle measures $\angle C$, $\angle A$, and side $a$ in triangle $ABC$ where $AB=20$ cm, $BC=19$ cm, and $\angle A=65^\circ$. Also find $\angle F$

1. **State the problem:** We are given a triangle ABC with sides AB = 10 cm, BC = 11 cm, and AC = 9 cm. We need to find the measures of angles \(\angle 4\), \(\angle B\), and \(\an

1. **Stating the problem:** We have triangle ABC with sides AC = 10 cm, BC = 11 cm, and the missing side AB = 2 cm. We need to find the measures of angles \(\angle 4\), \(\angle B\

1. **Problem:** Given triangle ABC with sides AB = 10 cm, BC = 11 cm, and side AC unknown, find the type of triangle and the measures of angles A, B, and C. 2. **Formula and rules:

1. **Problem Statement:** Find the missing side lengths and then use the Law of Cosines to find the indicated angles in triangles.

1. The problem is to find the formula for the volume of a cylinder. 2. The volume $V$ of a cylinder is given by the formula:

1. **Problem:** Given triangle with angles $m\angle B = 135^\circ$, $m\angle C = 30^\circ$, side $b = 35.2$ mm, find sides $a$, $c$ and triangle type. 2. **Formula:** Use Law of Si

1. **State the problem:** We need to find the volume of a cylinder with height $h=13$ feet and radius $r=11$ feet. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** Find the surface area of a sphere with radius $r = 10$ yards. 2. **Formula:** The surface area $A$ of a sphere is given by the formula:

1. **State the problem:** Find the total surface area of a sphere with radius $r=3$ ft. 2. **Formula:** The total surface area $A$ of a sphere is given by

1. **Problem statement:** We have a right triangle with legs of lengths 10 inches and 17 inches. We need to find the length of the hypotenuse. 2. **Formula used:** In a right trian

1. **State the problem:** We need to find the volume of a cone with height $h=12$ cm and radius $r=9$ cm. 2. **Formula:** The volume $V$ of a cone is given by the formula:

1. The problem asks which congruence rule explains why the two triangles GHJ and KMN are congruent. 2. The given information shows that in both triangles, two sides and the include

1. **State the problem:** We have two triangles, \(\triangle VWS\) and \(\triangle UST\), and we want to determine which congruence rule explains why these triangles are congruent.