Math Assignment Ch-12 Class X
Surface Area and Volumes

CBSE Maths Assignment on surface area and volume of cube, cuboid, cylinder, cone, sphere, hemisphere and frustum of cone for class X,   Extra questions on surface area and volume.

Note  :- For solving the problems related to the surface area and volume students need the knowledge of unit conversion. For important unit conversion tables click here

  

QUESTION 1

If the radius of the base of a right circular cylinder is halved, keeping the height same, then find the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder. 

[Answer  1/4]

               

QUESTION 2

Total surface area of a cube is 216 cm², find its volume.  

[Answer 216cm³]

QUESTION 3

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs 3.50 /m² .  

[Ans Rs 5365.80]

QUESTION 4

A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base radius  r.  Find the height of water in the cylindrical  flask. 

[Ans h/3m²]

QUESTION 5

The volume of hemisphere is 2425.5 cm². Find its curved surface area. 

[Ans 693 cm²]

QUESTION 6

A right angled triangle whose sides are 3cm, 4cm and 5cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two cones so formed. Also, find their curved surfaces.

QUESTION 7

The diameters of internal and external surfaces of a hollow spherical shell are   6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of length 8/3 cm , find the diameters of the cylinder.  

 [Ans 14 cm]

QUESTION 8

The cost of painting the total outside surface of a closed cylindrical tank at 60 paise per square dm is Rs 237.60. The height of the tank is 6 times the radius of the base of   the tank. Find the volume upto two decimal places.   

[Ans 509.14 dm³]

       

QUESTION 9

The interior of the building is in the form of cylinder of diameter 4.3 m and height 3.8 m surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and the volume of the building. Take π= 3.14 

Ans [71.83 m²  , 65.55 m³]

QUESTION 10

A solid composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10/dm².    

[Ans Rs 457.60]

QUESTION 11

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21cm and its volume is 2/3 of the volume of the hemisphere. Calculate the height of the cone and the surface area of the toy.  

Ans [28 cm,  5082 cm²]

QUESTION 12

What length of the solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm.   

Ans [79 cm]

QUESTION 13

A well of diameter 2 m is dug 14m deep. The earth taken out it has been spread evenly all around it to form an embankment of height 40 cm. Find the width of embankment.      

Ans [5 m]

QUESTION 14

2.2 dm³ of brass is to be drawn into a cylindrical wire 0.25 cm in diameter . Find the length of the wire. 

Ans [448 m]

QUESTION 15

How many spherical bullets each of 5 cm in diameter can be cast from a rectangular block of metal  11 dm x 1 m x 5 dm.  

Ans [8400 bullets]

QUESTION 16

An agriculture field is in the form of a rectangle of length 20m and width 14m. A 10 m deep well of diameter 7m is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in its level.     

Ans  [1.594 m]

Hint [Area of field - 𝝅r² ] x h = Volume of the earth taken out from the well ]

QUESTION 17

50 circular plates each of diameter 14 cm and thickness 0.5 cm are placed one above the other to form  a right circular cylinder. Find the total surface area ?        

Ans  [1408 cm²]

QUESTION 18

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm ?    

Ans [190.93 cm³]

QUESTION 19

Prove that the surface area of the sphere is equal to the curved surface of circumscribed cylinder.

QUESTION 20

The radius of the solid iron sphere is  8 cm. Eight rings of iron plate of external radius 20/3 cm and thickness 3cm are made by melting  this sphere. Find the internal diameter of each ring. 

Ans [4 cm]

QUESTION 21

Metal spheres each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm when 16 spheres are packed in the box. which is filled with preservative liquid . Find the volume of the liquid ? Use π = 669/213          

Ans  [448 cm³]

QUESTION 22

Rain water, which falls on a flat rectangular surface of length 6m and breadth 4m is transferred into a cylindrical vessel of internal radius  20cm. What will be the  height of water in the cylindrical vessel if a rainfall of 1 cm has fallen.

Ans [191cm]

QUESTION 23

A conical vessel of radius 6 cm and height 8 cm is completely filled with water.  A sphere is lowered into the water and its size is such that when it touches the sides it is just immersed as shown in the figure. What fraction of the water flows out.       

[Ans   3 : 8 ]

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QUESTIONS DELETED FROM CBSE SYLLABUS

QUESTION 21

The height of the right circular cone is trisected by two planes drawn parallel to the base. Show that the volumes of the three portions  starting from the top are in the ratio  1: 7 : 19

QUESTION 22

A shuttle cock used for playing badminton has the shape of a frustum of cone mounted on a hemi-sphere. The external diameter of the frustum are 5 cm and 2 cm, the height of the entire shuttle cock is  7 cm. Find its external surface area.       [74.26 cm²]      

QUESTION 23

A solid cone of base radius 10 cm is cut into 2 parts through the mid-points of its heights ,by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone.

                        

Level 3

QUESTION 24

A bucket made up of a metal sheet is in the form of a frustum of cone of height 16cm with diameters of its lower and upper ends are 16 cm and 40 cm respectively Find the volume of the bucket . Also, find the cost of the bucket if the cost of metal sheet used in Rs20 per 100cm² use  π = 3.14  [10449.92 cm³,  Rs 391.87]

                                                                     

QUESTION 25

The perimeters of the ends of a frustum are 48 cm and 36 cm. If the height of the frustum be 11 cm, find its volume.       [1554 cm³]

QUESTION 27

The height of the cone is 30 cm. A small cone is cut off at the top by the plane parallel to the base . If its volume be 1/27 of the volume of the given cone, at what   height above the base is the section made.      [20 cm]

QUESTION 28

 If a cone is cut into two parts by a horizontal plane passing through the mid points of its axis, find the ratio of the volumes of the upper part and the cone. [1:8]

QUESTION 29

The radii of the bases of two right circular solid cones of same height are r₁ and r₂ respectively. The cones are melted and recast into a solid sphere of radius R. Show that the height of the cone is given by \[h=\frac{4r^{3}}{r_{1}^{2}+r_{2}^{2}}\]

                                                                                                                          

QUESTION 30

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 into which the altitude of the cone is divided by the plane.   [ 1 : 2 ]

  

QUESTION 31

A cone is cut by a plane parallel to its base and the upper part is removed. If the curved surface area of the remainder (frustum) is 15/16  times the curved surface area of the whole cone, then find the ratio of the line segments to which the cone’s height is divided by the plane.   [1 : 3]

Important Result for frustum of cone

In  △ AEF and △ ADC

∠1 = ∠2  .......( Each = 90 degree)

∠3 = ∠3  ...........( common angle )

∴ by AA ~ rule                                

△ AEF ~ △ ADC                        

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