ICSE Class 10

General instructions: Answer all questions. Marks are shown in brackets [ ].

Objective

1. 1.
   Ratio of volumes of two cones with same radii is

   1. a. $h_1:h_2$
   2. b. $s_1:s_2$
   3. c. $r_1:r_2$
   4. d. None of these
   [1]
2. 2.
   If the volume of two spheres is in the ratio $27:64$, then the ratio of their radii is

   1. a. $3:4$
   2. b. $4:3$
   3. c. $9:16$
   4. d. $16:9$
   [1]
3. 3.
   A right circular cylinder of radius $r$ and height $h$ (where, $h > 2r$) just encloses a sphere of diameter

   1. a. $r$
   2. b. $2r$
   3. c. $h$
   4. d. $2h$
   [1]
4. 4.
   The diagram below shows a cone of maximum size carved out from a cube of edge 14 cm. Which labelled part in the diagram represents the **height** of the cone?

   1. A. The slant edge from the apex to the base circumference
   2. B. The vertical line from the apex to the center of the base
   3. C. The diameter of the circular base of the cone
   4. D. The curved surface connecting the apex to the base
   [1]
5. 5.
   A cone and a hemisphere have the same base and the same height. What is the ratio between their volumes?

   1. A. 1:2
   2. B. 2:3
   3. C. 3:4
   4. D. 1:3
   [1]
6. 6.
   If the perimeter of one face of a cube is $20\, \mathrm{cm}$, then its surface area is

   1. a. $120\mathrm{cm}^2$
   2. b. $150\mathrm{cm}^2$
   3. c. $125\mathrm{cm}^2$
   4. d. $400\mathrm{cm}^2$
   [1]
7. 7.
   A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. How many cones are recast?

   1. A. 200
   2. B. 250
   3. C. 270
   4. D. 300
   [1]
8. 8.
   The ratio of the base area to the curved surface area of a conical tent is 40:41. If its height is 18 m, what is the air capacity of the tent in terms of π?

   1. A. 38400π m³
   2. B. 12800π m³
   3. C. 48000π m³
   4. D. 9600π m³
   [1]
9. 9.
   A solid metallic sphere is melted and recast into smaller cones of radius 3.5 cm and height 3 cm. If the radius of the original sphere is 10.5 cm, find the number of cones obtained.

   1. A. 84
   2. B. 126
   3. C. 168
   4. D. 210
   [1]
10. 10.
    How many metres of canvas 1.25 m wide will be needed to make a conical tent whose base radius is 17.5 m and height 6 m?

    1. A. 814 m
    2. B. 654 m
    3. C. 1017.5 m
    4. D. 925 m
    [1]
11. 11.
    An open cylindrical vessel of internal diameter $7\mathrm{cm}$ and height $8\mathrm{cm}$ stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is $3.5\mathrm{cm}$ and height $8\mathrm{cm}$, as shown in the diagram: . When the vessel is filled with water, which labelled part of the diagram represents the volume of water required to fill the vessel?

    1. A. The entire internal volume of the cylinder
    2. B. The volume of the cylinder not occupied by the cone
    3. C. The volume of the cone alone
    4. D. The sum of the volumes of the cylinder and the cone
    [1]
12. 12.
    The circumference of the edge of a hemisphere bowl is 132 cm. When π is taken as 22/7, find the capacity of the bowl in cm³.

    1. A. 12580 cm³
    2. B. 22540 cm³
    3. C. 19404 cm³
    4. D. 16550 cm³
    [1]
13. 13.
    A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

    1. A. 7 cm
    2. B. 14 cm
    3. C. 21 cm
    4. D. 28 cm
    [1]
14. 14.
    A solid metallic cone of base radius 6 cm and height 10.125 cm is melted and recast into a sphere. What is the radius of the sphere?

    1. A. 3.0 cm
    2. B. 4.5 cm
    3. C. 6.0 cm
    4. D. 9.0 cm
    [1]
15. 15.
    The radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take π = 3.14)

    1. A. Radius = 5 cm, Slant height = 13 cm
    2. B. Radius = 10 cm, Slant height = 26 cm
    3. C. Radius = 15 cm, Slant height = 39 cm
    4. D. Radius = 8 cm, Slant height = 20 cm
    [1]
16. 16.
    The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. What is the length of the wire?

    1. A. 36 m
    2. B. 24 m
    3. C. 12 cm
    4. D. 16 m
    [1]
17. 17.
    A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top is 2.5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.25 cm, are dropped into the vessel, two-fifths of the water flows out. The number of lead shots dropped into the vessel is:

    1. A. 110
    2. B. 220
    3. C. 440
    4. D. 880
    [1]
18. 18.
    A hollow metal sphere of internal and external radii 2 cm and 4 cm respectively is melted into a solid cone of base radius 4 cm. What is the height and slant height of the cone?

    1. A. Height = 14 cm; Slant height = 14.56 cm
    2. B. Height = 7 cm; Slant height = 8.06 cm
    3. C. Height = 28 cm; Slant height = 28.43 cm
    4. D. Height = 12 cm; Slant height = 12.65 cm
    [1]
19. 19.
    A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is

    1. a. $\left(\frac{4}{3}\right)^{1 / 3}$
    2. b. $\left(\frac{8}{3}\right)^{1 / 3}$
    3. c. $(3)^{1 / 3}$
    4. d. $2$
    [1]
20. 20.
    A cone of maximum size is carved out from a cube of edge 14 cm. What is the surface area of the remaining solid after the cone is carved out?

    1. A. 1960 cm²
    2. B. 22379.28 cm²
    3. C. 2352 cm²
    4. D. 2464 cm²
    [1]