Mensuration
- A rectangular water tank is 80 metre × 40 metre. Water flows into it through a pipe of 40 sq.cm at the opening at a speed of 10 km/hr. The water level will rise in the tank in half an hour by
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Volume of water filled by pipe in 30 minutes
= 
40 × 1000000 
cu.cm. 2
= 20000000 cu. cm.∴ Height of water level = 20000000 = 5 cm. 8000 × 4000 8 Correct Option: D
Volume of water filled by pipe in 30 minutes
= 40 × 1000000 cu.cm. 2
= 20000000 cu. cm.∴ Height of water level = 20000000 = 5 cm. 8000 × 4000 8
- A solid cylinder has the total surface area 231 square cm. If its curved surface area is 2/3 of the total surface area, then the volume of the cylinder is
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Let the radius of cylinder be r cm.
Height = h cm.
According to the question,
2πrh + 2πr² = 231Again, 2πrh = 2 × 231 = 154 3
∴ 2πr² = 231 – 154⇒ 2 × 22 r² = 77 7 ⇒ r² = 77 × 7 = 49 22 × 2 2 × 2 ⇒ r = 7 cm. 2
∴ 2πrh = 154⇒ 2 × 22 × 7 × h = 154 7 2
⇒ 22h = 154⇒ h = 154 = 7 cm. 22
∴ Volume of cylinder = πr²h= 22 × 7 × 7 × 7 cu.cm. 7 2 2
= 269.5 cu. cm.Correct Option: C
Let the radius of cylinder be r cm.
Height = h cm.
According to the question,
2πrh + 2πr² = 231Again, 2πrh = 2 × 231 = 154 3
∴ 2πr² = 231 – 154⇒ 2 × 22 r² = 77 7 ⇒ r² = 77 × 7 = 49 22 × 2 2 × 2 ⇒ r = 7 cm. 2
∴ 2πrh = 154⇒ 2 × 22 × 7 × h = 154 7 2
⇒ 22h = 154⇒ h = 154 = 7 cm. 22
∴ Volume of cylinder = πr²h= 22 × 7 × 7 × 7 cu.cm. 7 2 2
= 269.5 cu. cm.
- A right circular cylinder having diameter 21 cm and height 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The number of such cones to be filled with ice cream is
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Total volume of ice-cream = πr²h
= π 21 ² × 39 cu.cm. 2 = 8379π cu.cm. 2
For a cone of ice-cream,Volume of cone = 1 π × 7 ² × 12 cu.cm. 3 2 ∴ Volume of hemi–sphere = 2 π × 7 ³ cu.cm. 3 2
Total volume of cone–shaped ice cream= π 49 × 12 + 343 cu.cm. 3 4 4 = π 147 + 343 cu.cm. 3 4 = π 588 + 343 cu.cm. 3 4 = π × 931 cu.cm. 3 4 ∴ Number of cones = 8379π × 3 × 4 = 54 2 π × 9 Correct Option: A
Total volume of ice-cream = πr²h
= π 21 ² × 39 cu.cm. 2 = 8379π cu.cm. 2
For a cone of ice-cream,Volume of cone = 1 π × 7 ² × 12 cu.cm. 3 2 ∴ Volume of hemi–sphere = 2 π × 7 ³ cu.cm. 3 2
Total volume of cone–shaped ice cream= π 49 × 12 + 343 cu.cm. 3 4 4 = π 147 + 343 cu.cm. 3 4 = π 588 + 343 cu.cm. 3 4 = π × 931 cu.cm. 3 4 ∴ Number of cones = 8379π × 3 × 4 = 54 2 π × 9
- THe sides of a rectangle with dimension 7 cm × 11 cm are joined to form a cylinder with height 11 cm. What is the volume of this cylinder?
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According to the question, 2πr = 7
⇒ 2 × 22 × r = 7 7 ⇒ r = 7 × 7 cm. 2 × 22
∴ Volume of Cylinder = πr²h= 22 × 7 × 7 × 7 × 11 7 2 × 22 × 2 × 22 = 7 × 7 × 7 = 42.875 cu.cm. 8 Correct Option: D
According to the question, 2πr = 7
⇒ 2 × 22 × r = 7 7 ⇒ r = 7 × 7 cm. 2 × 22
∴ Volume of Cylinder = πr²h= 22 × 7 × 7 × 7 × 11 7 2 × 22 × 2 × 22 = 7 × 7 × 7 = 42.875 cu.cm. 8
- A spherical aquarium can accommodate 11 fishes, and each fish requires 1.54 cu. metre of water. What is the volume of the aquarium ?
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Volume of spherical aquarium = (11 × 1.54) cu. metre
= 16.94 cu. metreCorrect Option: B
Volume of spherical aquarium = (11 × 1.54) cu. metre
= 16.94 cu. metre
