Volume - problems
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- Volume and body diagonal
Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
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.
- Conical area
A right angled triangle has sides a=11 and b=10 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
- Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
- Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
- Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately?
- Cube in a sphere
The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
- Transforming cuboid
Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length?
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
Water pipe has a cross-section 1420 cm2. An hour has passed 831 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 8 hours if water flow same speed?
Fire tank has cuboid shape with a rectangular floor measuring 11 m × 14.3 m. Water depth is 1.3 m. Water was pumped from the tank into barrels with a capacity of 3.9 hl. How many barrels were used, if the water level in the tank fallen 3 cm? Wri
Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
- Density - simple example
Material of density of 1278 kg/m3 occupies a container volume of 80 cm3. What is its mass?
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.