Surface area - 9th grade (14y) - examples
- Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
- Cube surface area
The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
- 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.
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?
How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material.
Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
- 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.
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″.
- 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.
The top of the tower is a regular hexagonal pyramid with base edge 9.2 meters long and a height 9.6 meters. How many m2 of sheet is required to cover the top of the tower if we count 12% of the sheet waste?
- Cylinder - basics
Cylinder with base radius r = 37 cm and height h=74 cm. Calculate:
- Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=37 cm, r2=40 cm and its distance v=20 cm.
Cylinder shell has the same content as one of its base. Cylinder height is 25 m. What is the radius of the base of the cylinder?
- Pyramid roof
1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm3. What is the area of surface of the prism?
- Rotary cone
The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.