Area of shape + volume - math problems

Number of problems found: 96

Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
The trench
Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.
Alcohol from potatoes
In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol?
Wooden box
The block-shaped box was placed on the ground, leaving a rectangular print with dimensions of 3 m and 2 m. When flipped over to another wall, a print with dimensions of 0.5 m and 3 m remained in the sand. What is the volume of the wooden box?
Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm², the base edge is 20 cm long. Calculate the volume of the prism
Round flowerbed
Around a round flowerbed with a diameter of 6 meters and I will make a sidewalk up to 0.5 meters wide. How much gravel is needed if the layer is to be 5 cm high?
Fire tank
1428 hl of water is filled in a block-shaped fire tank with the edges of the base 12 m and 7 m. Calculate the content of water-wetted areas.
Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
Cardboard box
Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
Triangular prism,
The regular triangular prism, whose edges are identical, has a surface of 2514 cm ^ 2 (square). Find the volume of this body in cm³ (l).
Hexa pyramid
The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
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.
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 edg
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?
Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
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.
Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.