📐 geometry

1. **Find the volume of the rectangular prism with dimensions 4 cm, 5.1 cm, and 9 cm.** The formula for the volume of a rectangular prism is:

1. **State the problem:** We need to find the depth (height) of the inside of a microwave oven given its volume in cubic feet and its width and length in inches. 2. **Given:**

1. **State the problem:** We have a quadrilateral □PQRS with perimeter 144 and the condition that PQ = QR. 2. **Define variables:** Let the length of PQ = QR = $x$.

1. **State the problem:** We need to find the total volume of a wedding tent composed of a right rectangular prism and a rectangular pyramid on top. 2. **Identify dimensions:**

1. **State the problem:** We have a triangular prism with a rectangular base of length 40 and width 29, and a triangular face with base 29 and height $h$. The height $h$ is given a

1. **State the problem:** We need to find the volume of a cone with a height of 25 meters and a radius of 11.5 meters.

1. **Problem Statement:** Calculate the volume of a cone with height $25$ m and radius $11.5$ m. 2. **Formula:** The volume $V$ of a cone is given by

1. **State the problem:** We want to find the area of a regular octagon, which is a polygon with 8 equal sides and 8 equal angles. 2. **Formula used:** The area $A$ of a regular po

1. **State the problem:** We need to find the volume of a sphere with a diameter of 57.1 cm, rounded to the nearest tenth of a cubic centimeter. 2. **Formula:** The volume $V$ of a

1. **State the problem:** We are given a right triangle with legs 24 and 18. A segment inside the triangle divides the right vertical side (length 18) into two parts labeled $2x+1$

1. **State the problem:** We are given a cube with volume 350 cm³ and need to find the edge length expressed as a radical and as a power. 2. **Recall the formula:** The volume $V$

1. **State the problem:** We are given triangle BCD with circumcenter H inside it. Known lengths are EC = 7, HF = 3, HB = 13, and BD = 24. We need to find the missing segment lengt

1. **Problem Statement:** Given four triangles Q, R, S, and T with angles and side lengths as follows: - Triangle Q: angles 65°, 45°, and one unknown; side length 10 opposite 65°.

1. The problem asks which postulate or theorem can be used to prove the congruence of two right triangles HIJ and STQ. 2. Given information:

1. **Problem statement:** Given a circle with center $O$, diameter $AB$, and point $S$ on the circumference such that $\angle BOS = \theta$, with $OA = OB = r$ and $OD = x$. We nee

1. **State the problem:** Given triangle TUV with circumcenter Z, and segments XU=19, ZW=15, ZV=21, and VU=34, find the missing segment lengths WV and TV. 2. **Recall properties of

1. **State the problem:** Given that lines QS and TV are parallel, prove that $m\angle VUW + m\angle PRS = 180^\circ$. 2. **Recall the given information and theorems:**

1. **Problem statement:** We have triangle ABC with sides AB = 5 cm, CB = 11 cm, and angle A = 113°. We need to find the measure of angle C. 2. **Formula used:** We will use the La

1. **State the problem:** We have a right triangle ABC with a right angle at C. Side AC is 14 ft, side CB is 21 ft, and angle C is 89° (approximately a right angle). We need to fin

1. **State the problem:** Complete the proof that the lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{QS}$ are parallel. 2. **Given:** $\angle VUW \cong \angle PRQ$ (Given

1. The problem is to find the radius $r$ of a circle given its area $A = 25$ cm² and the formula for the area of a circle $A = \pi r^2$. 2. The formula for the area of a circle is: