Sample Paper - 2008

Class- X

Subject – Mathematics

Surface Areas and volumes

Class- X

Subject – Mathematics

Surface Areas and volumes

1) Two cubes of 12cm edge are joined end to end. Find the surface area of the resulting cuboid.

2) Three cubes of sides 6 cm edge are joined end to end. Find the surface area of the resulting cuboid.

3) A solid sphere of radius 6cm is melted and recast into small spherical balls each of diameter 0.6cm. Find the number of balls thus obtained.

4) A sphere of diameter 7 cm is dropped in a right circular cylinder vessel partly filled with water. The diameter of the cylindrical vessel is 14 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

5) A hemispherical bowl of internal diameter 40 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 4 cm and height 8 cm. How many bottles are required to empty the bowl?

6) A conical vessel whose internal radius is 6cm and height is 25cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises.

7) A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone. Find the ratio of the line-segment in which the cone’s altitude is divided by the plane.

8.) How many spherical bullets can be made out of a solid cube of lead whose edge measures 55cm, each bullet being 10 cm in diameter?

9.) A sphere of diameter 7 cm is dropped in a right circular cylinder vessel partly filled with water. The diameter of the cylindrical vessel is 14 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

10.) A circus tent is cylindrical upto a height of 3m and conical above. If the diameter of the base is 105m and vertical height of the conical part is 7.26 m. Find the total canvas used in making the tent.

11.) A toy is in the shape of a right circular cylinder with a hemisphere on one end and cone on the other. The radius and height of the cylindrical part are 5cm and 13cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the cone is 30cm.

12.) The radii of the circular ends of a conical bucket which is 49cm high, are 35cm and 14cm. Find the capacity of the bucket.