NCERT Mathematics Class 10 Exemplar Ch 12 Surface Areas and Volumes Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Three metallic solid cubes whose edges are , and are melted and formed into a single cube. Find the edge of the cube so formed.


2. How many shots each having diameter can be made from a cuboidal lead solid of dimensions ?

Answer: 84

3. A bucket is in the form of a frustum of a cone and holds litres of water. The radii of the top and bottom are and , respectively. Find the height of the bucket.


4. A cone of radius and height is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.


5. Two identical cubes each of volume are joined together end to end. What is the surface area of the resulting cuboid?


6. From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.


7. Two cones with same base radius and height are joined together along their bases. Find the surface area of the shape so formed.

Answer: (approx.)

8. Two solid cones A and B are placed in a cylindrical tube as shown in the Fig. 12.9. The ratio of their capacities is . Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

Two Solid Cones Are Placed in a Cylindrical Tube

Answer: , ; , ;

9. An ice cream cone full of ice cream having radius and height as shown in the Fig. 12.10. Calculate the volume of ice cream, provided that its part is left unfilled with ice cream.

An Ice Cream Cone Full of Ice Cream


10. Marbles of diameter are dropped into a cylindrical beaker of diameter containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by .

Answer: 150

11. How many spherical lead shots each of diameter can be obtained from a solid rectangular lead piece with dimensions , and .


12. How many spherical lead shots of diameter can be made out of a solid cube of lead whose edge measures .


13. A wall long, thick and high is constructed with the bricks each of dimensions . If the mortar occupies th of the volume of the wall, then find the number of bricks used in constructing the wall.


14. Find the number of metallic circular disc with base diameter and of height to be melted to form a right circular cylinder of height and diameter .


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