📐 geometry

1. **State the problem:** Find the total surface area of the given triangular prism with triangular base sides 13 cm, 5 cm, and 16 cm, height 12 cm, and length (depth) 30 cm. 2. **

1. **State the problem:** We need to find the volume of an L-shaped prism. It can be divided into two rectangular prisms: one big prism minus a smaller cutout prism. 2. **Identify

1. The problem asks for the volume of oil in a cylindrical tank that is half-full. 2. Volume of a full cylinder is given by the formula $$V = \pi r^2 h$$, where $r$ is the base rad

1. **State the problem:** We have a cuboid-shaped community hall with dimensions 30 m (length), 15 m (width), and 3 m (height).

1. **Problem Statement:** Find the volume of a sphere with diameter 21 cm. The formula for the volume of a sphere is $$\text{Vol} = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 2

1. The problem asks to find the surface area of a cylinder given its net, which consists of two circles and one rectangle. 2. Given:

1. **Problem:** Calculate the curved surface area and the total surface area of a cylinder with radius $r=6$ cm and height $h=5$ cm. Round each answer to 1 decimal place. 2. **Reca

1. We are given two circles each with diameter 23 mm and a rectangle with height 19 mm. 2. First, calculate the radius of each circle: $$r = \frac{23}{2} = 11.5 \text{ mm}$$

1. The problem is to find the surface area of a cylinder given the net dimensions: radius $r=9.5$ mm and height $h=17$ mm. 2. The formula for the surface area of a cylinder is $$\t

1. The problem asks to find the curved surface area of a cylinder with height $16$ cm and radius $5$ cm. 2. The curved surface area $A$ of a cylinder is given by the formula:

1. The user requests to draw the angle, which is a graphical task rather than a purely mathematical one. 2. Since the request lacks specific details like angle size or context, I c

1. **State the problem:** We have the formula for the volume $V$ of a cone: $$V = \frac{1}{3} \pi r^2 h$$

1. **Find the volume of a cone with height 6 in and radius 1 in** (since diameter is 2 in, radius is half): Formula for the volume of a cone: $$V = \frac{1}{3}\pi r^2 h$$

1. **State the problem:** We are given the volume formula of a cone:

1. The problem gives a trapezoid divided into two figures: a smaller trapezoid on the left with sides labeled 3, 7, and 11, and a rectangle on the right with an unknown width label

1. **Problem statement:** We need to find the angle $y$ in a triangle given a $67^\circ$ angle at the top vertex and two sides marked equal, with a parallel line to the base passin

1. The problem involves a trapezoid connected to a rectangle with given side lengths labeled as 3, 1, and 7. 2. The trapezoid has top-left vertical side = 3, bottom-left vertical s

1. সমস্যা: একটি আয়তাকার মাঠের দৈর্ঘ্য 4.0 মিটার এবং প্রস্থ 0.4 মিটার। মাঠের চারপাশ দিয়ে হাঁটতে সময় লাগে 3 মিনিট 30 সেকেন্ড। মাঠের পরিধি এবং হাঁটার গতি নির্ণয় কর। 2. মাঠের পরিধি

1. **State the problem:** Find the value of angle $x$ in a right triangle where the right angle is $90^\circ$, two smaller arcs inside the right angle measure $\alpha^\circ$ each,

1. **State the problem:** Given a circle passing through points A, B, D, E, F and tangents at B and D meeting at C, express the angles \(\overline{B_2}, \overline{D_4}, \overline{C

1. **Find q in triangle PQR** Given that triangle PQR is right-angled at Q, with side PQ = 4, angle R = 45°, and hypotenuse PR = q.