# 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. Ratio of volumes If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
2. Pile of sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
3. Earth's circumference Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
4. Allan Allan keeps tropical fish. His aquarium is 4 feet long, 1 foot wide, and 2 feet tall. Each fish needs at least 0.5ft³ of water. What is the maximum number of fish that he can keep in the aquarium? Please show your solution. Please
5. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
6. Closed drum Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm . (π= 3.14)
7. Ribbon on the cube A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches).
8. Water depth How many square meters of the inside of the pool wet the water if the pool is 25 meters long and 10 meters wide and the water depth is 1.2 meters everywhere.
9. Seat How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
10. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
11. Aquarium The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edge
12. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
13. Steel tube The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
14. Right circular cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
15. Jared's room painting Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet high. There are two windows that measure 6 feet by 5 feet each. There are two doors, whose dimensions are 30 inches by 6 feet each. If a gallon of pa

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