📐 geometry

1. The problem asks to draw the outline of each view of a 3D prism: Plan View, Front Elevation, and Side Elevation. 2. The Plan View shows the shape as viewed from above. We projec

1. **Problem statement:** Pour 1.5 liters of water into a cuboid tank with length 25 cm, width 10 cm, and height 16 cm. Find the depth of the water in cm. 2. **Convert volume from

1. **State the problem:** We have an 8-sided shape ABCDEFGH with given side lengths and height. We know the total area is 434 cm². We want to find the length of side CD. 2. **Ident

1. **State the problem:** We have a circle with center P, with diameters AC and BD. The angle between radii PA and PD is given as 155°. 2. Since AC and BD are diameters, point A is

1. **State the problem:** We need to find the volume of a prism whose cross-section consists of two rectangles joined in an L-shape.

1. Find the volume of a rectangular prism with length 17 ft, width 3 ft, and height 21 ft. The formula for the volume of a rectangular prism is:

1. The user asks for the formula involving \(\pi r^2\), which is the formula for the area of a circle. 2. The formula to calculate the area \(A\) of a circle with radius \(r\) is g

1. Problem: Find the surface area of a cone with height $16$ ft and radius $12$ ft. Calculate slant height $l$ using Pythagoras: $$l = \sqrt{16^2 + 12^2} = \sqrt{256 + 144} = \sqrt

1. Problem: Find the surface area of a cone with height 16 ft and base diameter 12 ft. Step 1: Calculate the radius $r$ of the base: $r = \frac{12}{2} = 6$ ft.

1. **Surface Area of a Cone**: Given height $h=16$ ft and base diameter $d=12$ ft, so radius $r=\frac{12}{2}=6$ ft. Calculate the slant height $l$ using Pythagoras theorem: $$l=\sq

1. The problem is to find the area of a semicircle with a diameter of length 2 units. 2. Recall the formula for the area of a full circle: $$A=\pi r^{2}$$, where $r$ is the radius.

1. Stating the problem: We have a rectangular prism (Package B) with height $h = 10$ cm, breadth $b = 10$ cm, and length $l = 20$ cm. We will calculate:

1. Stating the problem: We need to verify by calculation that the area of a rectangular cardboard sheet is 1600 cm^2 given its dimensions: Height = 10 cm, Base = 10 cm, Length = 20

1. The problem involves a quadrilateral GFVH inscribed in a circle with given angle measures at points V and H, and an external or arc angle near G of 168°. 2. We are asked to find

1. The problem involves creating equations of circles to describe a flower pattern and related artistic elements. 2. For each circle, the standard form equation is $$(x - h)^2 + (y

1. **Problem Statement:** Create an artwork using circles and represent each circle with its equation in standard form $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $h,k$ are the center

1. **Nyatakan masalah**: Diberi segi tiga dengan titik A, B, C, dan D, dengan BCD garis lurus. Panjang AB = 7 cm, AD = 10 cm, sudut \( \angle ACD = 85^\circ \), dan sudut \( \angle

1. Given a triangle PQR with sides $PQ = 12$ cm, $QR = 9$ cm, and $PR = 18$ cm, we need to find the angle $\theta$ at vertex $Q$ between sides $PQ$ and $QR$. 2. We can use the Law

1. The problem involves creating an artistic design using circles by applying concepts of circle equations, centers, and radii. 2. The flower consists of one large center circle an

1. **Problem Statement:** Create and label a flower design with circles using their standard equations. You will describe centers and radii and write the equation in the form $$ (x

1. Problem 1: Find the measure of arc AN. Given angles inside circle R are 100°, 65°, and 30°. AE is a diameter. Arc AN measure can be either 65° or 30°, depending on interpretatio