Body volume - 9th grade (14y) - examples
- 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%?
- 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 =?
- Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
- 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.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
- 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?
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?
- Spherical cap
From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere?
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
- Sand pile
Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c
From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
- Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 61%.
Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.