# Equation + area - math problems

#### Number of problems found: 159

• The pool
The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?
• How many
How many different rectangles with integer page lengths have an area S = 60 cm²?
• Railway embankment
The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
• Area and perimeter of rectangle
The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
• Dimensions of the trapezoid
One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2
• Sow barley
Farmers wanted to sow barley within 13 days. Due to the excellent weather, they exceeded the daily plan of sowing by 2 ha and therefore finished sow grain in 12 days. How many hectares of land did they sow with barley?
• Shell area cy
The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
• The cylinder
The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.
• Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
• Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
• Side lengths
In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
• A map
A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
• An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Hectares of forest
12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area?
• Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• Tiles
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 of these tiles have so that no tile remains?
• Two gardens
The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
• Three faces of a cuboid
The diagonal of three faces of a cuboid are 13,√281, and 20 units. Then the total surface area of the cuboid is.

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