📐 geometry

1. **Stating the problem:** We are given a circle with diameter BC perpendicular to chord DE at point F. We know BC = 12 inches, DE = 10 inches, AC = 6 inches, DA = 7.1 inches, FE

1. **Problem Statement:** Determine the surface area of the 3-D object made up of two right pyramids with rectangular bases. 2. **Understanding the Object:** The object consists of

1. **Problem:** Find the perimeter and area of a polygon with sides 12 in, 6.4 in, 4.6 in, 9 in, and 9 in. 2. **Formula:**

1. **State the problem:** Find the volume of a cylinder given radius $r=5$ mm and height $h=25.5$ mm.

1. **State the problem:** We have a cylinder-shaped candy container with volume $125.6$ cubic centimeters and height $10$ centimeters. We need to find the radius $r$ of the contain

1. **Stating the problem:** Calculate the volume of a cylinder with diameter $d=8$ cm.

1. **State the problem:** Calculate the volume of a cylinder with diameter $d=12$ inches and height $h=4$ inches. 2. **Formula:** The volume $V$ of a cylinder is given by

1. **Problem statement:** Find the locus of the midpoints of all chords of length 6 inches in a circle of radius 5 inches. 2. **Key concept:** The midpoint of a chord lies on a lin

1. **State the problem:** Find the volume of a cylinder with radius $r=5$ mm and height $h=25.5$ mm. 2. **Formula:** The volume $V$ of a cylinder is given by $$V=\pi r^2 h$$ where

1. **Problem:** Which of the following correctly describes the steps to find the volume of a cylinder? 2. **Formula:** The volume $V$ of a cylinder is given by $$V = Bh$$ where $B$

1. Problem 6: Find the area of the shaded region inside a circle with an inscribed rectangle. Given: Top side of rectangle = 13 ft, bottom diameter of circle = 14 ft, left side of

1. **Problem statement:** The light on a lighthouse can reach a maximum distance of 20 miles and rotates 360 degrees. We need to find the total area illuminated by the light. 2. **

1. **Problem 9:** Find the perimeter and area of a semicircle with diameter 5.2 ft. 2. **Formula:**

1. **Stating the problem:** We are given a geometry figure with intersecting lines and several angles labeled with values or expressions. We need to find the measures of angles $\a

1. **State the problem:** We are given an equation involving angles: $ (3x - 5) + (7x + 5) = 180 $. We need to find the value of $x$. 2. **Formula and rules:** The sum of adjacent

1. **State the problem:** We need to find the volume of a stepped compound rectangular prism with given dimensions. 2. **Understand the shape:** The figure is composed of two recta

1. **State the problem:** We need to find the measure of the major arc $m\widehat{VXW}$ in a circle centered at $U$ with points $V$, $X$, and $W$ on the circle. $V$ and $W$ lie on

1. **State the problem:** We have a rectangle with one side length 20 cm and the other side length $x$ cm. The area is given as 400 cm$^2$, both area and length are accurate to 2 s

1. **State the problem:** We need to determine which of the given statements about a circle's radius, diameter, and circumference are true. 2. **Recall key formulas and definitions

1. **State the problem:** We need to find the circumference of a circle given its diameter is 24 cm. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. **Problem:** Find the length |BE| to 1 decimal place. 2. **Given:** The diagram shows points B, E, and other points with distances 3.1 m, 5.4 m, 9.2 m, and 10.67 m.