📐 geometry

1. **Problem:** Find the surface area of a square pyramid with base edges 11 in and slant height 20.7 in. 2. **Formula:** Surface area of a pyramid = Base area + Lateral area

1. **Problem statement:** We need to find the area of the logo on the work suit, which is shaped as shown with dimensions $a=28$ cm, $b=3$ cm, and $c=23$ cm. 2. **Understanding the

1. **State the problem:** Whitney wants to find the surface area of a bird feeder made of two coaxial cylinders, one on top of the other. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the volume of a cylinder with diameter 26.8 cm and height 9.8 cm. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We need to find the volume of a sphere with a diameter of 22 yards. 2. **Formula for the volume of a sphere:**

1. **State the problem:** Find the volume of a sphere with radius $r=8$ meters. 2. **Formula:** The volume $V$ of a sphere is given by

1. **State the problem:** We have a trapezoid with perimeter $P = 150$ cm and area $A = 0.12$ m². We want to find possible lengths for its bases and height. 2. **Convert units:** S

1. **Stating the problem:** We need to find the area of a parallelogram given its diagonals and one side length. 2. **Formula used:** The area of a parallelogram can be found using

1. **State the problem:** Calculate the volume of a sphere with radius $r=10$ meters. 2. **Formula for the volume of a sphere:**

1. **State the problem:** Calculate the volume of a cone with radius $r=4$ inches and height $h=10$ inches. 2. **Formula:** The volume $V$ of a cone is given by

1. **State the problem:** We want to find how many moving boxes of dimensions 620 mm x 300 mm x 330 mm can fit inside a van with internal dimensions 2.50 m (length) x 1.26 m (width

1. **Problem statement:** Given points A, B, C, D, E and their images A', B', C', D', E' after translations described by movements in "Kästchen" (grid squares).

1. **State the problem:** Find the diameter of the base of a cone given its volume $V = 24\pi$ cubic feet and height $h = 2$ feet. 2. **Formula for the volume of a cone:**

1. The problem is to show that the angles in a triangle sum to 180° using angle facts. 2. We start by drawing a triangle with angles labeled $x$, $y$, and $z$.

1. **State the problem:** Three angles fit around a point, meaning their sum is 360°. Two of the angles are 112° and 57°. We need to find the size of the third angle and classify i

1. **State the problem:** We have a triangle with a height of $1 \frac{5}{8}$ inches (which is $1.625$ inches), a base length of $4 \frac{1}{2}$ inches (which is $4.5$ inches), and

1. **Problem 31:** Given triangle ABC with angles $m\angle A = X$, $m\angle B = 2X$, and $m\angle C = 2X + 30^\circ$. Find $m\angle B$. 2. The sum of angles in any triangle is $180

1. **State the problem:** We have a right triangle PON with sides PO = 7, PN = 9.3, and a right angle at O. We need to find the angle $x$ at point N. 2. **Formula used:** In a righ

1. **Problem statement:** We have a right triangle PON with a right angle at O. Side PO is 7 units, side PN is 9.3 units, and we want to find the angle $x^\circ$ at vertex N. 2. **

1. **State the problem:** We have a right triangle CBA with a right angle at B. Side CB is 4.6 units, side CA (the hypotenuse) is 9 units, and we want to find angle $x^\circ$ at ve

1. The problem is to analyze a triangle where angle B is given as 90 degrees. 2. Knowing that angle B is 90 degrees means the triangle is a right triangle with angle B as the right