Download Worksheet 6 1. The distance between the centers of two adjacent

Worksheet 6
1. The distance between the centers of two adjacent faces of a cube is 8 cm. What is the
length of the edges of the cube? What is the volume of the cube?
2. The areas of different faces of a cuboid are 15cm2, 33cm2 and 67cm2. What is the volume
of the solid?
3. The volume of a cuboid is 36cm3, the length of its diagonals is 7cm and the length of one
of its edges is 6cm. What are the lengths of the other edges of the solid?
4.
The volume of a square prism is 19.845dm3 and the perimeter of the base is 84cm. What
is the surface area of the solid?
5. The length of each of the edges of a triangular prism is 10cm. What are the volume and
the surface area of the solid?
6. The base of a prism is a symmetrical trapezium, the lengths of its parallel sides are 21cm
and 16cm, the lengths of the legs are 9cm. What are the surface area and the volume of the
prism if its height is 10cm?
7. The length of the sides of the base of a hexagonal pyramid is 9cm. The height of the solid
is 15cm. What are the surface area and the volume of the pyramid?
8. The length of the sides of the base of a square pyramid is 12cm. The angle between the
base and one lateral face is 60. What are the surface area and the volume of the pyramid?
9. The height of a sqare pyramid is 21cm, the length of the sides of the square is 40cm. What
are the surface area and the volume of the pyramid? What is the length of the lateral edges
of the pyramid?
10. The area of one of the faces of a regular tetrahedron is 17cm2. What is the volume of the
solid?
11. The edges at a common vertex of a tetrahedron are perpendicular to each other. The
lengths of these edges arev 12cm, 18cm and 32cm. Calculate the surface area and the
volume of the tetrahedron.
12. The sides of the base of a regular octagonal pyramid is 8cm. The angle between the lateral
edges and the base is 46. What are the surface area and the volume of the solid?
13. The surface area of a truncated square pyramid is 2873cm2. The base and the top side
lengths are 32cm and 9cm. Calculate the volume of the solid.
14. The diameter of the base of a right circular cylinder is equal to its height. What are the
surface area and the volume of the solid if the radius is 8cm?
15. 480cm2 of a metal sheet was used to make a cylindrical vessel with opened top. What is
the volume of the vessel if the radius of the base is 6cm?
16. The lateral surface of a cylinder is laid flat so that it becomes a square with sides of 42cm.
What is the volume of the cylinder?
17. What are the surface area and the volume of a cone if the slant height is 10cm and the
radius of the circular base is 6cm?
18. The lateral surface of a cone is laid flat and formed a quarter of a circle. Calculate the ratio
between the radius and the height.
19. The radius of a cone is 24cm, the height is 36cm. A small cone is cut from this cone by a
plane parallel to the base of the cone. The distance of this plane from the base of the cone
is 12cm. What are the surface area and the volume of the truncated cone?
20. What is the radius of a sphere if its surface area is 1978.92cm2.
21. What is the distance of a plane from the center of a sphere, if the radius of the sphere is
10cm and radius of the intersected circle is 5cm?
22. The radii of three lead balls are 5cm, 8cm and 12cm. The three balls are melted into one
ball. What is the radius of this new ball?