# Solid geometry, stereometry - page 14

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry deals with 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.

- Sphere radius

The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm. - Cuboid box

Cuboid box have dimensions of 30 cm, 25 cm and 40 cm. Sketch its network and compute surface area of box. - Volume increase

How many percent will increase in the pool 50 m, width 15m if the level rises from 1m to 150cm? - Cylindrical tank

Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder. - Cube 1-2-3

Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm. - Three cubes

The body was created by gluing three identical cubes. Its volume is 192 cm^{3}. What is its surface in dm^{2}? - Volume and area

What is the volume of a cube which has area of 361 cm^{2}? - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Two cuboids

Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm - Surface of cubes

Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes? - Cubes into cuboid

How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8,4dm and 4,8? - Scale factor

A prism with a volume of 1458 mm^{3}is scaled down to a volume of 16mm^{3}. What is the scale factor in fraction form? - Inscribed sphere

How many percents of the cube volume takes the sphere inscribed into it? - Water block

A block with a 50 cm^{2}base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water? - Ratio

The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height. - Volume of cube

Solve the volume of a cube with width 26cm . - Stones in aquarium

In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes) - Cube, cuboid, and sphere

Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere? - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Cuboid - Vab

Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.

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