📐 geometry

1. **State the problem:** We need to find the height $h$ of a cylinder given its volume $V = 668.6944$ m³ and radius $r = 4.4$ m. 2. **Formula used:** The volume of a cylinder is g

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

1. The problem asks for the volume $V$ of a cylinder in terms of its diameter $d$ and height $h$. 2. The formula for the volume of a cylinder is given by:

1. **State the problem:** We need to approximate the volume of a cylinder with radius $r=2$ cm and height $h=12$ cm. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** Find the area of the given shape with dimensions 2.1 inches and 6.8 inches. 2. **Identify the shape:** Since only two dimensions are given and no other de

1. The problem states that the area of a triangle is $\frac{32}{15}$ square centimeters and the height is $\frac{3}{4}$ centimeters. We need to find the length of the base. 2. Reca

1. **State the problem:** We need to find the area of a rectangle with given side lengths 4.6 ft and 8.4 ft. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. **State the problem:** We are given the area of a triangle as 16.28 square feet and the height as 3.7 feet. We need to find the length of the base. 2. **Formula used:** The area

1. **State the problem:** We are given the area of a triangle as $\frac{25}{3}$ square centimeters and the height as $\frac{2}{5}$ cm. We need to find the length of the base expres

1. The problem states that the area of a triangle is $\frac{25}{3}$ square centimeters and the height is $\frac{2}{5}$ cm. We need to find the length of the base. 2. Recall the for

1. The problem is to understand and use the formula for the volume of a cylinder, which is given by $$V = r^2 \cdot \pi \cdot h$$ where $V$ is the volume, $r$ is the radius of the

1. **State the problem:** We are given two similar triangles \(\triangle STU\) and \(\triangle FEG\) with angles and side lengths labeled. We need to complete the similarity statem

1. **State the problem:** We are given two similar triangles \(\triangle GHI\) and \(\triangle EDF\) with angles and side lengths labeled. We need to complete the similarity statem

1. The problem asks if the angle $b$ is 62° in the given circle diagram where $u=124$ and $b=62$ are indicated. 2. In circle geometry, the sum of angles around a point is 360°.

1. **Stating the problem:** We are given angles in a circle or polygon with some known and unknown angles labeled as $a$, $b$, $c$, and $d$. The values given are $a=124^\circ$, $b=

1. **Problem:** Given a rectangle with diagonal $c=13$ cm and height $h=8$ cm, find the area $A$. 2. **Formula:** For a rectangle, area $A = \text{length} \times \text{height}$. Th

1. **State the problem:** We are given four models, each with three squares attached to a triangle. The areas of the squares are given, and we need to determine which model can be

1. The problem asks for the coordinates of triangle XYZ after two transformations: reflection across the y-axis and then translation two units to the right. 2. Reflection across th

1. The problem states that triangles ABD and ACE are similar right triangles and asks which ratio explains why the slope of AB equals the slope of AC. 2. Recall that the slope of a

1. **Problem statement:** Calculate the length of the ferry route AB across the river given triangle ABC with \(\angle CBA = 90^\circ\), \(\angle ACB = 42^\circ\), and \(BC = 40\)

1. **Problem statement:** We have triangle $\triangle DEF$ with medians $DK$, $EL$, and $FJ$ intersecting at centroid $M$. Given lengths are $ML=9$, $MJ=8$, and $DK=24$. We need to