# 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.

1. Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
2. 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.
3. 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.
4. 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
5. Distance of lines Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
6. A pipe A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?
7. 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?
8. 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?
9. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. 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 cm2.
11. 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.
12. 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.
13. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
14. The aquarium The aquarium has a capacity of 18 liters. What is its height when the square bottom is 8 2/3 cm long? The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?
16. 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
17. 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?
18. 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.
19. 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.
20. 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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