Pythagorean theorem + area of a shape - practice problems - page 18 of 23
Number of problems found: 456
- Calculate 74024
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Cone-shaped 44161
How many square meters of roofing is needed to cover the cone-shaped roof, if the perimeter of its base is 15.7m and a height of 30dm - Quadrilateral 16603
Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 8 cm and the length of the side edge h = 9 cm. - Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm.
- Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Church roof
The roof of the church tower has the shape of a regular tetrahedral pyramid with a base edge length of 5.4 meters and a height of 5 m. It was found that the 27% covering of the roof area needs to be corrected. What amount of material will be required? - 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? - 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. - Hexagonal 66574
The candle is made from wax in the shape of a regular hexagonal pyramid. It has a height of 6.5 cm and a length of the base edge of 3 cm. Find the volume of wax.
- Quadrilateral 19413
Calculate the surface area of a regular quadrilateral pyramid given: a= 3.2 cm h= 19 cm Method: 1) calculation of the height of the side wall 2) content of the base 3) shell contents 4) the surface of a regular quadrilateral pyramid - Quadrilateral 15023
The regular quadrilateral pyramid has a base circumference of 44 cm and a body height of 3.2 cm. Calculate its volume and surface. - Triangular 6610
The shell of the rotating cylinder is four times larger than the contents of its base. Determine the volume of the regular triangular prism inscribed in the cylinder. The radius of the bottom of the cylinder is 10 cm. - Right-angled 6034
A three-sided prism has a base in the shape of a right-angled triangle with a length of 5 cm. The giant wall of the prism shell has a volume of 104 cm². The prism is 8 cm high. Calculate the volume and surface area of the prism. - 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.
- Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Perpendicular prism network
Find the volume and surface of a triangular prism with the base of a right triangle, the network of which is 4 cm 3 cm (perpendiculars) and nine centimeters (height of the prism). - Hexagonal prism
The prism's base is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
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