# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.- Pyramid height

Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm. - Metal tube

Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g. - Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m. - Paper box

Calculate whether 11 dm² of paper is sufficient for gluing a box without a lid with bottom dimensions of 2 dm and 15 cm and 12 cm high. Write result as: 0 = No, 1 = Yes - Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - A pipe

A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume? - Height of the room

Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room? - A box

A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R? - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - Masquerade ball

Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm^{2}. - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Right triangular prism

We have cuboid with a base and dimensions of 12 cm and 5 cm and height of 4 cm. The tablecloth cut it into two identical triangular prisms with right triangular bases. The surface of the created prisms was painted with color. Calculate the surface area of. - The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm^{2}. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone - The aquarium

The aquarium has a capacity of 18 liters. What is its height when the square bottom is 8 2/3 cm long? - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm^{2}of material will we need when we 10% is waste? - Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and - Square prism

A square prism has a base with a length of 23 centimeters, what is the area in square centimeters of the base of the prism? - Paper box

Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper. - Iron density

Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3. - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.

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