# 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. Regular triangular pyramid Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
2. Butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain? The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
4. Prism 4 sides The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
5. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
6. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
7. Regular prism The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
8. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
9. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
10. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
11. Perpendicular prism Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs.
12. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
13. Density of the concrete Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
14. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
15. Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
16. The pot The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
17. Deviation of the lines Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
18. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
19. Water level How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
20. Pool The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, the bottom and walls of the pool must be painted. How many m2 of paint should

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