📐 geometry

1. **State the problem:** We need to find the hypotenuse of a right triangle when the other two sides are 25 and 95. 2. **Formula used:** According to the Pythagorean theorem, the

1. **State the problem:** We have a closed cylindrical hot water tank with volume 300 litres. We want to find the height $h$ in terms of $\pi$ and $r$, and then show the total surf

1. **Problem statement:** Determine the effect on volume when dimensions of cubes, cylinders, and rectangular prisms are changed as described. 2. **Formulas:**

1. **Problem 1: Calculate the value of the pronumeral $x$ using Pythagoras' Theorem.** 2. Pythagoras' Theorem states that in a right triangle, the square of the hypotenuse ($c$) eq

1. **State the problem:** We have a right triangle with a base segment of 11.4 cm, an extended base segment of 7.1 cm, a hypotenuse of 12.2 cm, and an unknown height $x$. We need t

1. The problem is to find the formula for the surface area of a sphere. 2. The formula for the surface area $A$ of a sphere with radius $r$ is:

1. The problem asks for the equation for the diameter of a circle. 2. Recall that the diameter of a circle is the length of a straight line passing through the center of the circle

1. **Stating the problem:** We need to match the sides of a right-angled triangle relative to the angle $\theta$. The triangle has a right angle, and $\theta$ is one of the other a

1. The problem asks to match the sides of a right triangle relative to the angle $\theta$. 2. In a right triangle, the hypotenuse is always the longest side opposite the right angl

1. **Énoncé du problème e)** Déterminer la perpendiculaire commune entre la diagonale $BD'$ et la diagonale de face $A'C'$ dans un cube d'arête $a$, puis calculer la distance entre

1. **State the problem:** We need to complete the table using the formula for arc length $$s = r\theta$$ where $$r$$ is the radius, $$\theta$$ is the angle in radians, and $$s$$ is

1. **State the problem:** Find the area of a square with side length 5. 2. **Formula:** The area $A$ of a square with side length $s$ is given by:

1. **State the problem:** We need to find the arc length $s$ using the formula $s = r\theta$, where $r$ is the radius and $\theta$ is the angle in radians. 2. **Convert the angle f

1. **Problem Statement:** Find the value of $x$ given two polygons with sides labeled $x+5$, 4 and 5, 15 respectively, assuming the polygons are similar and corresponding sides are

1. **State the problem:** We need to complete the table using the formula for arc length $$s = r\theta$$ where $$r$$ is the radius and $$\theta$$ is the angle in radians. We will c

1. **State the problem:** We need to find the number of radians in a central angle whose arc length is 23 of a circle, expressed in terms of $\pi$ radians and rounded to three sign

1. **State the problem:** Calculate the area of the house, the driveway, and the yard given the total property area and dimensions. 2. **Given:**

1. **Problem Statement:** We have a trapezoid with two vertical sides labeled $y$ inches and $x$ inches, and a horizontal base of 14 inches. The trapezoid has a right angle at the

1. The problem states that point N is the incenter of triangle ABC, and we are given expressions for segments ND and NE. We need to find NF. 2. Since N is the incenter, it is equid

1. **Problem statement:** Given a quadrilateral WXYZ with diagonals WX and WR, and the lengths XZ = 46 and WR = 21, find the length WX. 2. **Understanding the problem:** We are giv

1. **Problem Statement:** Find the area of the irregular shape with a rectangular cut-out on the top-left side, given side lengths labeled as $x+5$, $3$, $x-2$, and $x$. 2. **Under