# Body volume + surface area - examples - page 5

1. Cuboid - edges
The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
3. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
4. Rotary bodies
The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
5. Prism - eq triangle
Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
6. Octahedron
All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
7. Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
8. Cube
One cube has edge increased 5 times. How many times will larger its surface area and volume?
9. Cuboid surface
Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
10. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
11. Regular quadrilateral pyramid
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
12. Cuboid
Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
13. Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
14. Surface of cuboid
Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
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 =?
16. Cube walls
Find the volume and surface area of the cube if the area of one wall is 40cm2.
17. Cube 1-2-3
Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
18. Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
19. Conical area
A right angled triangle has sides a=12 and b=19 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.
20. Volume and area
What is the volume of a cube which has area of 361 cm2?

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