CBSE Class 10 Mathematics Surface Area And Volume Notes Set B

Question. The radius of a sphere (in cm) whose volume is 12p cm³, is:
(a) 3
(b) 3√3
(c) 32/3
(d) 31/3
Answer : C

Question. A cylindrical pencil sharpened at one edge is a combination of:
(a) a cone and a cylinder
(b) frustum of a cone and a cylinder
(c) a hemisphere and a cylinder
(d) two cylinders. 
Answer : A

Question. A surahi is a combination of:
(a) a sphere and a cylinder
(b) a hemisphere and a cylinder
(c) two hemispheres
(d) a cylinder and a cone.
Answer : A

Question. A plumbline (Sahul) is a combination of (see the given figure)

(a) a cone and a cylinder
(b) a hemisphere and a cone
(c) frustum of a cone and a cylinder
(d) sphere and cylinder
Answer : B

Question. The shape of a gilli, in the gilli-danda game (see the given figure), is a combination of

(a) two cylinders
(b) a cone and a cylinder
(c) two cones and a cylinder
(d) two cylinders and a cone
Answer : C

Question. A shuttle cock used for playing badminton has the shape of a combination of:
(a) a cylinder and a sphere
(b) a cylinder and a hemisphere
(c) a sphere and a cone
(d) frustum of a cone and a hemisphere
Answer : D

Question. A metallic sphere of diameter 20 cm is recast into a right circular cone of base radius 10 cm. What is the height of the cone?
(a) 4 cm
(b) 40 cm
(c) 60 cm
(d) 120 cm
Answer : B

Question. Three cubes each of side 15 cm are joined end to end. The total surface area of the cuboid is:
(a) 3150 cm²
(b) 1575 cm²
(c) 1012.5 cm²
(d) 576.4 cm²
Answer : A

Question. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is:
(a) 142296
(b) 142396
(c) 142496
(d) 142596
Answer : A

Question. A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. The height of the cone is:
(a) 12 cm
(b) 14 cm
(c) 15 cm
(d) 18 cm
Answer : B

Question. A medicine -capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm. the capacity of the capsule is:
(a) 0.36 cm³
(b) 0.35 cm³
(c) 0.34 cm³
(d) 0.33 cm³
Answer : A

Question. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
(a) 3:4
(b) 4:3
(c) 9:16
(d) 16:9
Answer : D

Question. If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is increased by:
(a) 200%
(b) 500%
(c) 700%
(d) 800%
Answer : C

Question. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is:
(a) 2 : 1
(b) 1 : 2
(c) 1 : 3
(d) 3 : 1
Answer : A

Question. The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is:
(a) 60p cm²
(b) 68p cm²
(c) 120p cm²
(d) 136p cm²
Answer : D

Fill in the Blanks

Fill in the blanks/tables with suitable information:

Question. A spherical metal ball of radius 8 cm is melted to make 8 smaller identical balls. The radius of each new ball is .......................... cm.
Answer : 4 cm

Question. The total surface area of the given solid figure is .......................... .

Answer : πrl + 2πrh + πr²

Question. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is .......................... .
Answer : 2r

Question. The ratio between the volumes of two spheres is 8:27. Then, the ratio between their surface areas is .......................... .
Answer : 4 : 9

Question. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 cm. The length of the wire is .......................... .
Answer : 36 cm

Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, then the ratio of the volume of the reduced cylinder to that of the original cylinder is .......................... .
Answer : [1 : 4]

Question. If the length of each diagonal of a cube is doubled, then its volume become ................ times.
Answer : If the length of each diagonal of a cube is doubled, then its volume becomes eight times. Write True or False. 

Question. Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr². 
Answer : False.

Question. A solid ball is exactly fitted inside a cubical box of side a. The volume of the ball is (4/3) πa³ .
Answer : False.

Question. The capacity of a cylindrical vessel with a hemispherical portion raised upwards at the bottom as shown in the given figure is πr²/3 (3h - 2r)

Answer : True.

Surface Area and Volume

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