Mensuration
- Two cubes of sides 6 cm each are kept side by side to form a rectangular parallelopiped. The area (in sq. cm) of the whole surface of the rectangular parallelopiped is
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Length of parallelopiped = 12 cm.
breadth = 6 cm.
height = 6 cm.
∴ Total surface area = 2 (12 × 6 + 6 × 6 + 12 × 6) sq.cm.
= 2 (72 + 36 + 72) sq.cm.
= 360 sq.cm.Correct Option: B
Length of parallelopiped = 12 cm.
breadth = 6 cm.
height = 6 cm.
∴ Total surface area = 2 (12 × 6 + 6 × 6 + 12 × 6) sq.cm.
= 2 (72 + 36 + 72) sq.cm.
= 360 sq.cm.
- The diameter of a copper sphere is 1 8 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, the diameter of the wire is
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Volume of sphere = 4 πr³ 3 = 4 × π × 9 × 9 × 9 3
= 972π cu. cm
Let the radius of wire be R cm, then
πR² × 10800 = 972π⇒ R² = 972 = 0.09 10800
⇒ R = √0.09
= 0.3 cm
∴ Diameter = 2 × 0.3 = 0.6 cmCorrect Option: D
Volume of sphere = 4 πr³ 3 = 4 × π × 9 × 9 × 9 3
= 972π cu. cm
Let the radius of wire be R cm, then
πR² × 10800 = 972π⇒ R² = 972 = 0.09 10800
⇒ R = √0.09
= 0.3 cm
∴ Diameter = 2 × 0.3 = 0.6 cm
- 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
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If the length of wire be h cm, then
πr²h = 66⇒ 22 
1 
² × h = 66 7 20 ⇒ h = 66 × 400 × 7 = 8400 cm 22
= 84 metreCorrect Option: A
If the length of wire be h cm, then
πr²h = 66⇒ 22 1 ² × h = 66 7 20 ⇒ h = 66 × 400 × 7 = 8400 cm 22
= 84 metre
- Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled ?
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Water flowed in 1 hour through the pipe
= 22 × 10 × 10 × 3000 m² = 660 m³ 7 10000 7
Volume of circular/cylindrical cistern= 22 × 5 × 5 × 2 = 110 m³ 7 7 ∴ Required time = 1100 = hours 7 5 660 3 7 or 1 hour 2 × 60 minutes 3
or 1 hour 40 minutesCorrect Option: B
Water flowed in 1 hour through the pipe
= 22 × 10 × 10 × 3000 m² = 660 m³ 7 10000 7
Volume of circular/cylindrical cistern= 22 × 5 × 5 × 2 = 110 m³ 7 7 ∴ Required time = 1100 = hours 7 5 660 3 7 or 1 hour 2 × 60 minutes 3
or 1 hour 40 minutes
- The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall (in cm) is :
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Let amount of rainfall be 'x'
20 × 20 × x = 22 × 1² × 3.5 7 ⇒ x = 22 × 3.5 = 0.025 metre = 2.5 cm 7 × 22 × 20 Correct Option: B
Let amount of rainfall be 'x'
20 × 20 × x = 22 × 1² × 3.5 7 ⇒ x = 22 × 3.5 = 0.025 metre = 2.5 cm 7 × 22 × 20
