Solid geometry, stereometry - page 60 of 123
Number of problems found: 2442
- Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - Pillar - bricks
A brick pillar has the shape of a four-sided prism with an isosceles trapezoid base with parallel sides a = 55 cm and c = 33 cm, leg b = 33 cm, and trapezoid height vₐ = 32.1 cm. The pillar is 1.9 m high. How many bricks were used to build it if one brick - Rotary cylinder
In a rotating cylinder, the surface area S= 96 cm² (without the base) and the volume V= 192 cm cubic are given. Calculate its radius and height. - Diamond base
A prism with a rhombus-shaped base has base diagonals of 24 cm and 20 cm. Calculate the height of the prism if its volume is 9.6 dm³. - From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base, with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Jane modeled a rotating cone with a base diameter of 10 cm. How tall was Jane's cone? - Quadrilateral pyramid
In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the base's diagonal is 50 cm. Calculate the pyramid shell area. - Sphere from tree points
Equation of sphere with three-point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Cuboid - volume and areas
The cuboid has a volume of 250 cm3, a surface of 250 cm2, and one side 5 cm long. How do I calculate the remaining sides? - Cylinder height
Calculate the height of the cylinder based on its surface S and the radius of the base r. a) r = 2 cm, S = 120 cm² b) r = 7 dm, S = 4,000 dm² c) r = 0.2 m, S = 20 square meters - Prism
The volume of a tetrahedral prism is 2.43 m³. The prism's base is a parallelogram with a side of 2,5 dm and height ha = 18 cm. Calculate the height of the prism. - Cone paint calculation
Forty identical traffic cones with base diameter d = 36 cm and height v = 46 cm are to be painted orange on the outside (without base). How much do we pay for paint if we need 500 cm³ of paint to paint 1 m² and 1 liter of paint costs CZK 8? - Cost to Cover Prism
Calculate how much we will pay for the paper to cover the box in the shape of a three-sided prism with the base of a right-angled triangle; if the overhangs measure 12 cm and 1.6 decimeters, the hypotenuse measures 200 millimeters, the box is 27 centimete - Glass cocktail level
The cone-shaped glass has a volume of 2.5 dl and a diameter of 13 cm. How much cocktail is left in the glass if the level only reaches half the height of the glass? - Prism surface calculation
Calculate the surface area of a triangular prism with a height of 7 dm. Measures the edges of the triangular base 45 cm, 5 dm, 550 mm. - Pyramid volume calculation
The area of a regular quadrilateral pyramid's mantle is equal to twice its base's area. Calculate the pyramid's volume if the base edge's length is 20 dm. - Trench
The trench is a four-sided prism. The cross-section has a trapezoidal shape with bases of 4 m and 6 m, and the length of the trench is 30 m. What is the depth of the trench if we dig 60,000 l of soil? - Sugar minicubes
1 kg of cubed sugar consists of 840 cubes with an edge of 1.1 cm. Determine the sugar's density and the box's dimensions if the cubes are lined up in seven rows of nine cubes each. How many square meters of cardboard are needed to make 3000 boxes? - Insulate house
The property owner wants to insulate his house. The house has these dimensions of 12, and 12 m is 15 m high. The windows have six dimensions, 170 and 150 cm. Entrance doors are 250 and 170 cm in size. How many square meters of polystyrene does he need? - Bucket
How many Kč (Czech crowns) will you pay for the painting of a room in the shape of a cuboid with floor dimensions of 5 and 4 m, given the height of the room is 3 m. You will not paint the floor, the door space (210 x 90 cm), and the space behind the mirro - Cuboid cone volume
We used the same amount of paint to paint a cuboid with dimensions of 10 cm, 15 cm, and 3 cm to paint the shell of a cone whose radius is 8 cm. How tall is this cone? Calculate its volume in liters.
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