Area + angle - practice problems - page 13 of 15
Number of problems found: 293
- Juice box 2
The box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm, and 32 cm. Suppose the box stays at the smallest base juice level and reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below - The farmer field
The field has a parallelogram shape with dimensions side a = 67 m and height 387 m. Two and two sides are at an angle 67°. Calculate the acreage of the field in hectares. - Clock hands
The hands-on clock shows the time as 12 hours and 2 minutes. Three hours later, calculate the size of an acute angle between the clock hands. - Goat
The meadow is a circle with a radius r = 20 m. How long must a rope tie a goat to the pin on the meadow's perimeter to allow the goat to eat half of the meadow? - Trapezoid - diagonal
A trapezoid has a length of diagonal AC crossed with diagonal BD in the ratio of 2:1. The triangle created by points A, the cross point of diagonals S, and point D has an area 164 cm². What is the area of the trapezoid? - Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 30 degrees, |AB| = 15 cm. Calculate the volume of the prism. - Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 6.7 cm and a plane ABV, ABC has angle 32 degrees. - De Moivre's formula
There are two distinct complex numbers, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers. - ISO trapezium
Calculate the area of an isosceles trapezoid with base 50 long, leg 12 long, and with the angle between the base and leg 70 degrees. - Tower
The roof of the tower is a regular hexagonal pyramid with a base edge 5.7 meters long and a height 7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 4% of metal for waste. - House roof
The house's roof is a regular quadrilateral pyramid with a base edge 20 m. If the roof pitch is 38° and we calculate 12% of waste, connections, and overlapping of the area roof, how much m² is needed to cover the roof? - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c have dimensions in the ratio of 10:8:9. If you know that the diagonal wall AC is 75 cm, and the angle between AC and space diagonal AG is 30 degrees. - Hexagon A
Calculate the area of a regular hexagon inscribed in a circle with radius r=15 cm. - Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 5 cm and |CAB| = 41°. Calculate area of the trapezoid. - Circle arc
Calculate the circular arc area in m² where the diameter is 263 dm and the central angle is 40°. Please result round to three decimal places. - Hexagon
There is a regular hexagon ABCDEF. If the area of the triangle ABC is 10, what is the area of the hexagon ABCDEF? I do not know how to solve it simply.... - Without Euclid laws
Right triangle ABC with a right angle at the C has a=5 and hypotenuse c=22. Calculate the height h of this triangle without the use of Euclidean laws. - Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone. - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°?
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