📐 geometry

1. **State the problem:** We have a large cone with height $36$ cm and radius $10$ cm.

1. Let's analyze each house diagram carefully. 2. For the first house (top-left):

1. Given that points P, Q, and S lie on a Cartesian plane with PQ parallel to the x-axis and PQ equals 20 times the length of segment S. 2. Point S is at (-6,0), Q is at (k,8), and

1. We are asked to find the volume of an ice cream cone with radius $r=2$ inches and height $h=6$ inches. 2. The volume $V$ of a cone is given by the formula $$V = \frac{1}{3} \pi

1. **Problem statement:** We have points A(4,1) and B(2,5). For each point C with positive integer coordinates $C(x,y)$, define $d_C$ as the shortest distance to travel from A to C

1. **State the problem:** We have a solid formed by removing a hemisphere (radius $2x$ cm) from a cone (base radius $5x$ cm, height $6x$ cm). The volume of this solid is $6948\pi$

1. **Problem statement:** We have a sector OABC of a circle with the center at O. The angle at O (angle AOC) is 60°.

1. **State the problem:** Find the value of angle $x$ in quadrilateral $ABCD$ where angles at $D$ and $C$ are $40^\circ$ and $62^\circ$ respectively, and sides $AB=15.2$ m, $BC=12.

1. **State the problem:** We have a regular pentagon ABCDE and a point F outside the pentagon such that the angle \(\angle AEF = 96^\circ\). We need to find the size of the obtuse

1. The problem asks for the volume of water in a rectangular prism-shaped container. 2. The base dimensions of the container are given as 90 mm by 90 mm, and the height of the wate

1. The problem states we have a rectangle with length 8 meters and height 5 meters. 2. To find the perimeter of a rectangle, use the formula $$P = 2(\text{length} + \text{width})$$

1. Stating the problem: We have a parallelogram ABCD. 2. Draw diagonal $AC$.

1. The problem asks us to calculate the volume of a cone with radius $r=10$ cm and height $h=36$ cm. 2. The formula for the volume of a cone is given by

1. **State the problem:** We need to find the area of quadrilateral EFGH with sides EH = 8 cm (vertical), HG = 14 cm (horizontal), and GF = 2 cm (vertical). Angles EHG and GFE are

1. The problem is to identify which two shapes among A, B, C, D, E, and F are similar. 2. To check similarity, we compare corresponding angles and the ratios of corresponding sides

1. **State the problem:** We have a right triangle ABC with the right angle at A. Point D lies on AC such that $AD=3$ cm and $DC=5$ cm. Point E lies on CB such that $CE=EB$, and se

1. Probleem (a): Die oppervlakte van ʼn driehoek is 48 m² en die basis is 16 m. Bereken die hoogte. 2. Die formule vir die oppervlakte van ʼn driehoek is:

1. The problem asks: What are parallel lines? 2. Parallel lines are two or more lines in a plane that never intersect or meet, no matter how far they are extended.

1. The problem asks how many pairs of parallel lines a rectangle has. 2. Consider a rectangle—it has four sides.

1. The problem asks about the type of angles found in a square. 2. A square is defined as a quadrilateral with four equal sides.

1. The problem statement is to find the radius given some geometric or algebraic context. 2. Since "radius" is a term commonly used in circles, let's define radius $r$ as the dista