Surface area + Pythagorean theorem - practice problems - page 6 of 15
Number of problems found: 296
- Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Pyramid
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same, and their length is 12.5 cm. Calculate the surface of the pyramid. - 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). - Ratio-cuboid
The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - 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. - Cone container
The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need for making this package.
- Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Calculate 71374
Calculate the volume and surface of a cone whose base diameter is 6 cm and height is 0.9 dm. - Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere. - Rectangular 5798
The pyramid has a rectangular base with dimensions a = 5cm, b = 6cm. The side edges are identical; their length is h = 11cm. Calculate the surface of the pyramid. - Calculate 5789
Calculate the volume and surface of the rotating cone with the base radius r = 4.6dm and the height v = 230mm.
- Calculate 4689
The area of the rotating cone shell is 240 cm2, and the area of its base is 160 cm². Calculate the volume of this cone. - Regular quadrilateral pyramid
Find the surface area of a regular quadrilateral pyramid with a volume of 24 dm³ and a height of 45 cm. - Quadrilateral pyramid,
A quadrilateral pyramid has a rectangular base with 24 cm and 13 cm dimensions. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid - Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area). - Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which we cut the spherical cap.
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