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Q 1. Two cubes each of volume {tex} 64 \mathrm { cm } ^ { 3 } {/tex} are joined end to end. Find the volume of the resulting cuboid.
{tex} 148 \mathrm { cm } ^ { 3 } {/tex}
{tex} 128 \mathrm { cm } ^ { 3 } {/tex}
{tex} 182 \mathrm { cm } ^ { 3 } {/tex}
{tex} 821 \mathrm { cm } ^ { 3 } {/tex}
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Q 2. A conical vessel whose internal radius is {tex} 5 \mathrm { cm } {/tex} and height {tex} 24 \mathrm { cm } {/tex} is full of water. The water is emptied into a cylindrical vessel with internal radius {tex} 10 \mathrm { cm } . {/tex} What is the height to which the water rises
{tex} 2 \mathrm { cm } {/tex}
{tex} 3 \mathrm { cm } {/tex}
{tex} 1 \mathrm { cm } {/tex}
{tex} 4 \mathrm { cm } {/tex}
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Q 3. Diagonal of a cube is {tex} \sqrt { 6 } \mathrm { cm } . {/tex} Then its lateral surface area is:
{tex} 6 \sqrt { 6 } \mathrm { cm } ^ { 2 } {/tex}
{tex} 36 \mathrm { cm } ^ { 2 } {/tex}
{tex} 12 \mathrm { cm } ^ { 2 } {/tex}
{tex} 8 \mathrm { cm } ^ { 2 } {/tex}
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Q 4. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is {tex} 14 \mathrm { cm } {/tex} and the total height of the vessel is {tex} 13 \mathrm { cm } {/tex}, then what is the capacity of the vessel?
{tex} 1642.66 \mathrm { cm } ^ { 3 } {/tex}
{tex} 1462.66 \mathrm { cm } ^ { 3 } {/tex}
{tex} 1662.42 \mathrm { cm } ^ { 3 } {/tex}
{tex} 1246.26 \mathrm { cm } ^ { 3 } {/tex}
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Q 5. A cylinder of base diameter {tex} 8 \mathrm { cm } {/tex} and height {tex} 7 \mathrm { cm } {/tex} is dipped vertically one third in a bucket full of paints. How much area get painted?
{tex} 108.95 \mathrm { cm } ^ { 3 } {/tex}
{tex} 553.14 \mathrm { cm } ^ { 3 } {/tex}
{tex} 318.47 \mathrm { cm } ^ { 3 } {/tex}
{tex} 226.28 \mathrm { cm } ^ { 3 } {/tex}
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Q 6. {tex}12{/tex} spheres of the same size are made from melting a solid cylinder of {tex} 16 \mathrm { cm } {/tex} diameter and {tex} 2 \mathrm { cm } {/tex} height. The diameter of each sphere is
{tex} \sqrt { 3 } \mathrm { cm } {/tex}
{tex} 2 \mathrm { cm } {/tex}
{tex} 3 \mathrm { cm } {/tex}
{tex} 4 \mathrm { cm } {/tex}
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Q 7. Match the following:
| Column I | Column II |
|---|---|
| (A) Volume of hollow cylinder | (P) {tex} \sqrt { l ^ { 2 } + b ^ { 2 } + h ^ { 2 }}{/tex} |
| (B) Diagonal of cuboid | (Q){tex} { \pi r ( l + r ) }{/tex} |
| (C) Volume of hemisphere | (R) {tex}\pi h ( R ^ { 2 } - r ^ { 2 }{/tex} |
| (D) Total surface area of cone | (S) {tex} \frac { 4 } { 3 } \pi ( \frac { r ^ { 3 } } { 2 }){/tex} |
{tex} ( \mathrm { A } ) - ( \mathrm { R } ) {/tex}
{tex} ( \mathrm { B } ) - ( \mathrm { S } ) {/tex}
{tex} ( \mathrm { C } ) - ( \mathrm { Q } ) {/tex}
{tex} (\mathrm D ) - (\mathrm P ) {/tex}
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Q 8. The number of solid spheres, each of diameter {tex} 6 \mathrm { cm } {/tex} that could be moulded to form a solid metal cylinder of height {tex} 45 \mathrm { cm } {/tex} and diameter {tex} 4 \mathrm { cm } {/tex} is
3
4
5
6
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Q 9. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then radius of the base of the cone is
{tex} 2 r {/tex}
{tex} 3 r {/tex}
{tex}r{/tex}
{tex}4r{/tex}
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Q 10. The diameter of a sphere is {tex} 6 \mathrm { cm } {/tex}. It is melted and drawn into a wire of diameter {tex} 2 \mathrm { mm } {/tex}. The length of wire is
{tex} 12 \mathrm { m } {/tex}
{tex} 18 \mathrm { m } {/tex}
{tex} 36 \mathrm { m } {/tex}
{tex} 66 \mathrm { m } {/tex}
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Q 11. The areas of three adjacent faces of a cuboid are a, b and c. If its volume is {tex} \mathrm V {/tex} then
{tex} \mathrm { V } = \mathrm { abc } {/tex}
{tex} \mathrm { V } ^ { 2 } = \mathrm { abc } {/tex}
{tex} \mathrm { V } = \mathrm { a } ^ { 2 } \mathrm { b } ^ { 2 } \mathrm { c } ^ { 2 } {/tex}
{tex} \sqrt { \mathrm { V } } = \mathrm { a } ^ { 2 } \mathrm { b } ^ { 2 } \mathrm { c } ^ { 2 } {/tex}
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Q 12. A basket ball is just packed in a cube of side {tex} 20 \mathrm { cm } , {/tex} then the surface area of the basket ball is:
{tex} 120 \mathrm { cm } ^ { 2 } {/tex}
{tex} 2400 \mathrm { cm } ^ { 2 } {/tex}
{tex} 400 \pi \mathrm { cm } ^ { 2 } {/tex}
{tex} 1256 \mathrm { cm } ^ { 2 } {/tex}
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Q 13. A conical vessel has a capacity of {tex}3.3 \mathrm{litres}{/tex} of milk. If the height of the vessel is {tex} 3.5 \mathrm { cm } , {/tex} then the diameter of the base is
{tex} 15 \mathrm { cm } {/tex}
{tex} 30 \mathrm { cm } {/tex}
{tex} 35 \mathrm { cm } {/tex}
{tex} 60 \mathrm { cm } {/tex}
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Q 14. Match the following:
| Column I | Column II |
|---|---|
| (A) Ratio of the volume of a cone and sphere if each has the same diameter and same height | (P) 9:32 |
| (B) The radii of two cones are in the ratio 2:1 and their volumes are equal, then ratio of their heights is | (Q) 1:2 |
| (C) If the heights of two right circular cones are in the ratio 1:2 and the perimeters of their bases are in the ratio 3:4, then ratio of their volume is | (R) 1:4 |
| (D) A right circular cone and a right circular cylinder have equal base and equal height are in the ratio 5:12, the ratio of the total surface area of the cylinder to that of the cone is | (S) 17:9 |
{tex} ( \mathrm { A } ) - ( \mathrm { Q } ) {/tex}
{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}
{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}
{tex} (\mathrm D ) - (\mathrm R ) {/tex}
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Q 15. If 'l ', 'b' and 'h' of a cuboid are increased, decreased and increased by 1%, 3% and 2% respectively, then the volume of the cuboid ___________.
Increases
Decreases
Increases or decreases depending on original dimensions
Can't be calculated with given data
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Q 16. A cuboidal metal block of dimensions 20 cm {tex}\times{/tex} 16 cm {tex}\times{/tex} 12 cm weighs 6 kg. Find the weight of block of the same metal of size 10 cm {tex}\times{/tex} 8 cm {tex}\times{/tex} 8 cm.
3 kg
8 kg
7 kg
1 kg
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Q 17. The bottom, side and front areas of a rectangular box are known. The product of these areas is equal to
the volume of box
the square root of the volume
twice the volume
the square of the volume
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Q 18. A right circular cone has for its base a circle having he same radius as a given sphere. The volume of the cone is one half that of the sphere. The ratio of the altitude of the cone to the radius of its base is:
1 : 1
1 : 2
2 : 1
2 : 3