Solid geometry, stereometry - page 15

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.

1. Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
2. Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
3. Cuboid
The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
4. Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
5. Rainfall
A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
6. Cylinder-shaped vase
If the cylinder-shaped vase is filled with water up to 35 cm, it contains 1 liter of water. How much water will it contain if it is filled to a height of 45cm?
7. Rain
It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
8. A residential
A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the
9. Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
10. Volcano
The crater of a volcano is approximately in the shape of a cone of a base 3.1416 sq. Mi. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?
11. A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
12. Square prism
A square prism has a base with a length of 23 centimeters, what is the area in square centimeters of the base of the prism?
13. A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
14. Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
15. Surface area 6
Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch
16. The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
17. Body diagonal - cube
Calculate the surface and cube volume with body diagonal 15 cm long.
18. Water flow 2
How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour
19. Cube in a sphere
The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
20. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.

Do you have interesting mathematical problem that you can't solve it? Enter it and we can try to solve it.

To this e-mail address we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.

See also more information on Wikipedia.