Surface area - 8th grade (13y) - examples
- 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?
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
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.
- 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.
- 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.
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'
Gift box has rectangular shape with dimensions of 4×9×19 cm. Todd wants to cover with square paper with sides of 27 cm. How much paper left him?
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.
- 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?
- 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?
- Cylinder - basics
Cylinder with base radius r = 37 cm and height h=74 cm. Calculate:
- Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 7 cm.