Mensuration
- Each side of a cube is decreased by 25%. Find the ratio of the volumes of the original cube and the resulting cube.
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Edge of the original cube = x units
Edge of the new cube = 3x units 4 ∴ Required ratio = x³ 
10 
³ 4 = 4³ = 64 3³ 27 Correct Option: D
Edge of the original cube = x units
Edge of the new cube = 3x units 4 ∴ Required ratio = x³ 10 ³ 4 = 4³ = 64 3³ 27
- If water is freezed to become ice, its volume is increased by 10%, then if the ice is melted to water again, its volume will be decreased by :
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Percentage decrease = 10 × 100 100 + 10 = 100 = 9 1 % 11 11 Correct Option: B
Percentage decrease = 10 × 100 100 + 10 = 100 = 9 1 % 11 11
- If the radius of a right circular cylinder open at both the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface area of the cylinder thus formed
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Effective percentage change = x + y + xy % 100 = - 25 + 25 - 25 × 25 % 100
= –6.25%
Negative sign shows decrease.Correct Option: D
Effective percentage change = x + y + xy % 100 = - 25 + 25 - 25 × 25 % 100
= –6.25%
Negative sign shows decrease.
- The amount of concrete required to build a concrete cylindrical pillar whose base has a perimeter 8.8 metre and curved surface area 17.6 square metre, is (Take π = 22/7)
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Radius of the base of cylindrical pillar = r metre (let)
∴ 2πr = 8.8⇒ 2 × 22 × r = 8.8 7 ⇒ r = 8.8 × 7 = 1.4 metre 2 × 22
Again,
2πrh = 17.6
⇒ 8.8 × h = 17.6⇒ h = 17.6 = 2 metre 8.8
∴ Volume of concrete = πr²h= 22 × 1.4 × 1.4 × 2 cu.cm. 7
= 12.32 cu. metreCorrect Option: D
Radius of the base of cylindrical pillar = r metre (let)
∴ 2πr = 8.8⇒ 2 × 22 × r = 8.8 7 ⇒ r = 8.8 × 7 = 1.4 metre 2 × 22
Again,
2πrh = 17.6
⇒ 8.8 × h = 17.6⇒ h = 17.6 = 2 metre 8.8
∴ Volume of concrete = πr²h= 22 × 1.4 × 1.4 × 2 cu.cm. 7
= 12.32 cu. metre
- A big cube is formed by arranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area that is coloured is
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Total number of cubes = 160 + 56 = 216
Edge of cube = ³√216 = 6 units
Number of cubes without exposure = (6 – 2)³ = 64
These cubes will be inside the big cube. Remaining cubes = 160 – 64 = 96
Again number of cubes with one face outside = 6 × (4 × 4) = 96∴ Required percent = 96 × 100 216
= 44.44%Correct Option: B
Total number of cubes = 160 + 56 = 216
Edge of cube = ³√216 = 6 units
Number of cubes without exposure = (6 – 2)³ = 64
These cubes will be inside the big cube. Remaining cubes = 160 – 64 = 96
Again number of cubes with one face outside = 6 × (4 × 4) = 96∴ Required percent = 96 × 100 216
= 44.44%
