📐 geometry

1. **State the problem:** Calculate the surface area of a cuboid with dimensions height $h=30$ cm, width $w=23$ cm, and depth $d=11$ cm. 2. **Formula for surface area of a cuboid:*

1. **State the problem:** We need to find the length (height) of a cylinder given its radius and volume. 2. **Formula:** The volume $V$ of a cylinder is given by the formula:

1. **State the problem:** We need to find the volume of a cylinder with height $h = 40$ cm and diameter $d = 14$ cm. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We have a circle $k$ with center at $(-1, 3)$ and a point on the circle at $(2, 7)$. We need to find:

1. **State the problem:** We need to find the volume of a cylindrical tin of paint with radius $r=9$ cm and height $h=20$ cm. 2. **Formula for the volume of a cylinder:** The volum

1. Problem: Calculate the area of the first figure (an L-shaped figure composed of two rectangles). 2. Formula: Area of rectangle = length \times width.

1. **State the problem:** We need to find the volume of a cylinder with radius $r=4$ cm and length (height) $h=11$ cm. 2. **Formula for the volume of a cylinder:**

1. The problem asks to identify the point with coordinates $\left(4 \frac{1}{2}, 0\right)$. 2. Coordinates are given as $(x, y)$ where $x$ is the horizontal position and $y$ is the

1. The problem asks to identify which point has coordinates $(0, -4.5)$. 2. Coordinates are given in the form $(x, y)$ where $x$ is the horizontal position and $y$ is the vertical

1. **State the problem:** A landscaper needs to cover a yard 14 meters long and 8 meters wide with a layer of dirt 0.25 meters deep. We need to find how many 1 cubic meter bags of

1. **Problem statement:** We need to find the total length of a toy car track consisting of two quarter circles with radii 30 cm and 20 cm. 2. **Formula for arc length:** The lengt

1. **State the problem:** We need to find the volume of a cylinder with radius $r = 16.4$ m and height $h = 4.7$ m. 2. **Formula:** The volume $V$ of a cylinder is given by the for

1. **State the problem:** We have a right triangle with two 45° angles and one leg of length $\sqrt{2}$. We need to find the hypotenuse $x$. 2. **Recall the properties of a 45°-45°

1. The problem asks to find the angle number that forms a linear pair with \(\angle SXT\). 2. A linear pair of angles are two adjacent angles whose non-common sides form a straight

1. Let's clarify the problem: We are dealing with a circle where $AC$ is a segment related to the circle. 2. If $AC$ is a diameter, then its length is twice the radius. So if the r

1. The problem states that the distance around the edge of a circular swimming pool is 26 m. This distance is the circumference of the circle. 2. The formula for the circumference

1. **State the problem:** We need to find angle $\angle CAD$ in the circle where $AD$ is the diameter, given $\angle ACE = 36^\circ$ and $\angle ABC = 118^\circ$. 2. **Recall the k

1. **State the problem:** We have a right triangle with one side length 28 mm opposite a 60° angle, and we want to find the hypotenuse $s$. 2. **Recall the sine function:** In a ri

1. **State the problem:** We need to find the area of a stained glass window shaped like a rectangle with a quarter circle cut out from the top right corner, and a square inside th

1. The problem is to find the radius of a circle or sphere, but no specific details are given. 2. The radius $r$ is the distance from the center to any point on the circle or spher

1. **State the problem:** We need to find the volume of a cylindrical candle with radius $r$ cm and height 9 cm. 2. **Formula for volume of a cylinder:** The volume $V$ of a cylind