Solid geometry, stereometry - page 45 of 115
Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves the measurements of volumes of various solid figures (three-dimensional figures), including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.
Number of problems found: 2283
- Lampshade 7846
Lampshade for the face of a truncated cone with a height of 20 cm. The upper diameter of the shade is 13 cm, the lower 36 cm, and the side forms an angle of 60 degrees with the lower diameter. At least how much fabric is needed to make this shade? - Cross-section 5048
A path will lead to an embankment across the floodplain. The embankment will be 2 km long and have the shape of an isosceles trapezoid in cross-section with base lengths of 12 m and 8 m and a height of 2 m. Calculate the volume of material needed to build - Calculate 3
Calculate the cube volume whose edge is 3x-1,3x-1,3x-1 - Pool
The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, we must paint the bottom and walls of the pool. How many m² of paint should
- Calculating 63344
Calculate the volume of the cone formed by rotating an isosceles triangle about the height of the base. The triangle has a side length of 15 cm and a height to the base of 12 cm. When calculating, use the value pi = 3.14 and round the result to one decima - Spherical 63214
The gas tank consists of a 16m high cylinder with a diameter of 28m, which is closed at the top by a spherical canopy. The center of the spherical surface lies 4m below the bottom of the cylinder. Please calculate the spherical surface's radius and the ca - Dimensions 30651
How many tons of cement are needed to concrete two pillars 6.5 m high with a base in the shape of four squares joined into one cross of dimensions 1.2 m? 2.5 q of cement is needed for 1 cubic meter of concrete. - Quadrilateral 28491
Calculate the weight of a regular quadrilateral pyramid with a base edge of 4 cm in length and a body height of 6 cm if it is made of a material density of 8 g/cm³. - Cross-section 5558
How many m² of sheet metal is needed to cover 4 m high chimneys with a rectangular cross-section with dimensions of 2.5 m and 1.2 m? Add 1/20 to the folds.
- Cross-section 4507
How much soil needs to be removed when digging a 200-meter long ditch whose cross-section is an isosceles trapezoid with an area of 4812.5 cm²? - Cylinder-shaped 4411
A cylinder-shaped hole with a diameter of 12 cm is drilled into a block of height 50 cm with a square base with an edge length of 20 cm. The axis of this opening passes through the center of the base of the cuboid. Calculate the volume and surface area of - Painting 3328
The painter is to paint a room 7 m long, 4.5 m wide, and 3 m high. He charges CZK 27 per 1 m². How much do we pay painters for painting a room? - Bottom 3129
How many m² tiles do we need to line the walls and bottom of the pool in the shape of a block 25 m long, 10 m wide, and 180 cm deep? - The well
The well has the shape of a cylinder with a diameter of 2 m. From ground level to water level are 4 meters, and the water depth in the well is 6 m. How many m³ of soil did they dig when digging a well? How many liters of water is in the well?
- 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. - Elevation
What must be an observer's elevation so that he may see an object on the Earth 536 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km. - Dimensions 80746
The statements are sold in cardboard boxes – for example, the microwave oven box has dimensions of 52 cm, 32 cm, and 40 cm, and 0.4 m² of cardboard is added to the folds. How many square meters of cardboard are needed for 1,000 boxes? - Decorative 46721
How many liters of water can fit in a decorative garden tank in the shape of a regular hexagonal pyramid with a 30 cm long base edge? The depth of the tank is 30 cm. - Pepíček 39811
Pepíček went to school on the first day. Dad made him a paper cone for sweets in the shape of a cone with a side length of 50 cm and a base radius of 10 cm. How many cm² of paper did he need to make the cone?
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