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Q 1. A hemisphere and a cone have equal bases. If their height are also equal, then what is the ratio of their curved surfaces:
1 : 3
2 : 3
√2 : 1
None of these
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Q 2. A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
3 : 1 : 2
1 : 2 : 3
4 : 5 : 6
2 : 3 : 1
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Q 3. If {tex} r _ { 1 } {/tex} and {tex} r _ { 2 } {/tex} denote the radii of the circular bases of the frustrum of a cone such that {tex} r _ { 1 } > r _ { 2 } , {/tex} then write the ratio of the height of the cone of which the frustrum is a part to the height of the frustrum.
{tex} \frac { r _ { 1 } } { r _ { 1 } + r _ { 2 } } {/tex}
{tex} \frac { r _ { 1 } } { r _ { 1 } - r _ { 2 } } {/tex}
{tex} \sqrt { 2 }: 1 {/tex}
{tex} \sqrt { r _ { 1 } } / r _ { 2 } {/tex}
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Q 4. A metallic hemisphere is melted and recast in the shape of a cone with the same base radius {tex} R {/tex} as that of the hemisphere. If {tex} H {/tex} is the height of the cone, then the value of the {tex} H / R {/tex} is:
{tex} 1 / 2 {/tex}
{tex} 4 / 6 {/tex}
{tex} 1 / 3 {/tex}
{tex} 2 / 1 {/tex}
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Q 5. For the figure shown below match the column:
{tex}(\mathrm A) - (\mathrm Q ) {/tex}
{tex} ( \mathrm { B } ) - ( \mathrm { R } ) {/tex}
{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}
{tex} (\mathrm D ) - (\mathrm P ) {/tex}
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Q 6. There is a cylinder circumscribing the hemisphere such that their bases are common. The ratio of their volume is
1 : 3
1 : 2
2 : 3
3 : 4
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Q 7. The total surface area of a cube is numerically equal to the surface area of a sphere then the ratio of their volume is
{tex} \frac { \pi } { 6 } {/tex}
{tex} \sqrt { \frac { \pi } { 6 } } {/tex}
{tex} \frac { \pi } { 216 } {/tex}
{tex} \sqrt { \frac { 6 } { \pi } } {/tex}
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Q 8. If length, breadth and height of a cuboid is increased by {tex} x \% , y \% {/tex} and {tex} z \% {/tex} respectively. Then its volume is increased by:
{tex} \left[ x + y + z + \frac { x y + x z + y z } { 100 } + \frac { x y z } { ( 100 ) ^ { 2 } } \right] \% {/tex}
{tex} \left[ x + y + z + \frac { x y + x z + y z } { 100 } \right] \% {/tex}
{tex} \left[ x + y + z + \frac { x y z } { ( 100 ) ^ { 2 } } \right] \% {/tex}
None of these
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Q 9. Find the volume of a frustum of a cone whose height is {tex} 14 \mathrm { cm } {/tex} and the diameters of the circular base and top are {tex} 12 \mathrm { cm } {/tex} and {tex} 6 \mathrm { cm } {/tex} respectively
{tex} 896 \mathrm { cm } ^ { 3 } {/tex}
{tex} 1028 \mathrm { cm } ^ { 3 } {/tex}
{tex} 924 \mathrm { cm } ^ { 3 } {/tex}
{tex} 1236 \mathrm { cm } ^ { 3 } {/tex}
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Q 10. {tex}748{/tex} cubic cm of metal is used to make a metallic cylindrical pipe of length {tex} 14 \mathrm { cm } {/tex} and external radius {tex} 9 \mathrm { cm } . {/tex} Find its thickness
{tex} 2 \mathrm { cm } {/tex}
{tex} 2.5 \mathrm { cm } {/tex}
{tex} 1.5 \mathrm { cm } {/tex}
{tex} 1 \mathrm { cm } {/tex}
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Q 11. A hollow sphere of internal and external diameters {tex} 4 \mathrm { cm } {/tex} and {tex} 8 \mathrm { cm } {/tex} respectively is melted into a cone of base diameter {tex} 8 \mathrm { cm } . {/tex} Find the height of the cone
{tex} 14 \mathrm { cm } {/tex}
{tex} 12 \mathrm { cm } {/tex}
{tex} 16 \mathrm { cm } {/tex}
None of these
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Q 12. A cylindrical pencil sharpened at one edge is the combination of :
a cone and a cylinder
frustum of a cone and a cylinder
a hemisphere and a cylinder
two cylinders
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Q 13. A surahi is the combination of :
a sphere and a cylinder
a hemisphere and a cylinder
two hemispheres
a cylinder and a cone
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Q 14. A plumbline (Sahul) is the combination of :
a cone and a cylinder
a hemisphere and a cone
frustum of a cone and a cylinder
sphere and cylinder
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Q 15. A hollow cube of internal edge {tex} 22 \mathrm { cm } {/tex} is filled with spherical marbles of diameter {tex} 0.5 \mathrm { cm } {/tex} and it is assumed that {tex} \frac { 1 } { 8 } {/tex} space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is :
142296
142396
142496
142596
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Q 16. A medicine-capsule is in the shape of a cylinder of diameter {tex} 0.5 \mathrm { cm } {/tex} with two hemispheres stuck to each to its ends. The length of entire capsule is {tex} 2 \mathrm { cm } . {/tex} The capacity of the capsule is :
{tex} 0.36 \mathrm { cm } ^ { 3 } {/tex}
{tex} 0.35 \mathrm { cm } ^ { 3 } {/tex}
{tex} 0.34 \mathrm { cm } ^ { 3 } {/tex}
{tex} 0.33 \mathrm { cm } ^ { 3 } {/tex}
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Q 17. If two solid hemispheres of same base radius ' {tex} r {/tex} ' are joined together along their bases, then curved surface area of this new solid is:
{tex} 4 \pi r ^ { 2 } {/tex}
{tex} 6 \pi r ^ { 2 } {/tex}
{tex} 3 \pi r {/tex}
{tex} 8 \pi r^2 {/tex}
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Q 18. In a right circular cone, the cross-section made by a plane parallel to the base is a :
circle
frustum of a cone
sphere
hemisphere
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Q 19. Volumes of two spheres are in the ratio {tex} 64: 27 . {/tex} The ratio of their surface areas is :
3:4
4:3
9:16
16:9
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Q 20. The surface areas of two spheres are in the ratio 16: 9 . The ratio of their volumes is:
{tex}64:27 {/tex}
{tex}16:9 {/tex}
{tex}4:3 {/tex}
{tex} 16 ^ { 3 }: 9 ^ { 3 } {/tex}
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Q 21. A metallic spherical shell of internal and external diameters {tex} 4 \mathrm { cm } {/tex} and {tex} 8 \mathrm { cm } {/tex}, respectively, is melted and recast into the form of a cone of base diameter {tex} 8 \mathrm { cm } {/tex}. The height of the cone is:
{tex} 12 \mathrm { cm } {/tex}
{tex} 14 \mathrm { cm } {/tex}
{tex} 15 \mathrm { cm } {/tex}
{tex} 18 \mathrm { cm } {/tex}
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Q 22. A solid piece of iron in the form of a cuboid of dimensions {tex} 49 \mathrm { cm } \times 33 \mathrm { cm } \times 24 \mathrm { cm } , {/tex} is moulded to form a solid sphere. The radius of the sphere is :
{tex} 21 \mathrm { cm } {/tex}
{tex} 23 \mathrm { cm } {/tex}
{tex} 25 \mathrm { cm } {/tex}
{tex} 19 \mathrm { cm } {/tex}
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Q 23. A mason constructs a wall of dimensions {tex} 270 \mathrm { cm } \times {/tex} {tex} 300 \mathrm { cm } \times 350 \mathrm { cm } {/tex} with the bricks each of size {tex} 22.5 \mathrm { cm } \times 11.25 \mathrm { cm } \times 8.75 \mathrm { cm } {/tex} and it is assumed that {tex} 1 / 8 {/tex} space is covered by the mortar. Then the number of bricks used to construct the wall is:
11100
11200
11000
11300
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Q 24. Twelve solid sphere of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is :
{tex} 4 \mathrm { cm } {/tex}
{tex} 3 \mathrm { cm } {/tex}
{tex} 2 \mathrm { cm } {/tex}
{tex} 6 \mathrm { cm } {/tex}
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Q 25. A rectangular sheet of paper {tex} 40 \mathrm { cm } \times 22 \mathrm { cm } , {/tex} is rolled to form a hollow cylinder of height {tex} 40 \mathrm { cm } {/tex}. The radius of the cylinder (in {tex} \mathrm { cm } ) {/tex} is :
{tex}3.5{/tex}
{tex}7{/tex}
{tex} \frac { 80 } { 7 } {/tex}
{tex}5{/tex}
