# Volume - problems - page 7

1. Sphere
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
2. Cubic
Convert 660 m3 of natural gas volume to energy units kWh. Combustion of 1 cubic meter of natural gas is released energy 10.55 kWh.
The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
4. Ice cream in cone
In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
5. Stones in aquarium
In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
6. Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
7. Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
8. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
9. Cuboid 5
Calculate the weight of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (ς = 550 kg/m3).
10. Iron fence
One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
11. Granite cube
What is the weight in kg granite cube with an edge of 0.5 m if 1dm3 of granite weight 2600 g?
12. Surface of the cylinder
Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
13. Cube and water
How many liters of water can fit into a cube with an edge length of 0.11 m?
14. Cuboids in cube
How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
15. Cube 6
Volume of the cube is 216 cm3, calculate its surface area.
16. Water
On the lawn which has area 914 m2 rained 3 mm of water. How many liters of water rained?
17. Building base
Excavation for the building base is 350x600x26000. Calculate its volume in m3.
18. Beer
Which beer is better to drink: small beer (0.3 L) for 0.67 € or large (0.5 L) for 1.81 €?
19. Soil pit
Workers dug a pit cube with edge 2.5 meters. How many cars shall remove soil if the car suddenly take 4m³ of soil?
20. Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.

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