Area + Pythagorean theorem - practice problems - page 3 of 32
Number of problems found: 621
- Archaeologists 81478
Archaeologists need to find out the size of the vessel if the sherd found was in the shape of a circular section with a length of 12 cm and a height of 3 cm. What is the area of this section? - Determine 81311
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - Equilateral 81222
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere? - Circumference 81095
The hexagon pyramid has a circumference of 120 cm, and the length of the night edge is 25 cm. Calculate its volume. - Calculate 81034
Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r=5cm and the radius of the circular base of the segment ρ=4cm. - Right-angled 81019
In the right-angled triangle ABC (AB is the hypotenuse), a : b = 24 : 7, and the height to the side c = 12.6 cm applies. Calculate the lengths of the sides of triangle ABC. - The perimeter
The perimeter of the base of a regular quadrilateral pyramid is the same as its height. The pyramid has a volume of 288 dm³. Calculate its surface area round the result to the whole dm². - Consumption 80836
The right trapezoidal plot has a basic length of 102m and 86m. The vertical arm is 63 m long. Calculate the plot’s area and the mesh consumption for its fencing. - Arithmetic 80808
The lengths of the sides of a right triangle form the first 3 terms of the arithmetic sequence. The content is 6cm². - Right-angled 80745
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Equilateral 80573
The field has the shape of an equilateral triangle. Calculate its content if you know that the side is 280 meters long. - Airport's 80482
The plane flew from airport m on a course of 132° to airport n, then from n to p on a course of 235°. The distance between the airport's mn is 380 km, np 284 km. What will be the return course to m, and what is the distance between the airport's pm? - Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km. - Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - The perimeter
The perimeter of a rhombus whose diagonal lengths are in the ratio 3:4 is 40 cm. What is its area in cm²? - Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Constructed 77874
Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their contents are the same. - Isosceles triangle
Find the area of an isosceles triangle whose leg is twice the base, b=1 - A Pile of salt
A Pile of salt has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What area of the conical tarpaulin (a large sheet of material) is needed to cover the pile?
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