Mensuration
- Water flows at the rate of 10 metres per minute from a cylindrical pipe 5 mm in diameter. How long it take to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm ?
-
View Hint View Answer Discuss in Forum
Volume of water flowing from the pipe in 1 minute = π × 0.25 × 0.25 × 1000 cu.cm.
Volume of conical vessel = 1 π × 15 × 15 × 24 cu.cm 3 ∴ Required time = π × 15 × 15 × 24 = 28 minutes 48 seconds 3π × 0.25 × 0.25 × 1000 Correct Option: A
Volume of water flowing from the pipe in 1 minute = π × 0.25 × 0.25 × 1000 cu.cm.
Volume of conical vessel = 1 π × 15 × 15 × 24 cu.cm 3 ∴ Required time = π × 15 × 15 × 24 = 28 minutes 48 seconds 3π × 0.25 × 0.25 × 1000
- If a metallic cone of radius 30 cm and height 45 cm is melted and recast into metallic spheres of radius 5 cm, find the number of spheres.
-
View Hint View Answer Discuss in Forum
Volume of metallic cone = 1 πr²h 3 = 1 π × 30 × 30 × 45 cu.cm 3 Volume of a sphere = 1 πR³ 3 = 4 π × 5 × 5 × 5 3 ∴ Required number of spheres = 1 π × 30 × 30 × 45 = 81 3 4 π × 5 × 5 × 5 3 Correct Option: A
Volume of metallic cone = 1 πr²h 3 = 1 π × 30 × 30 × 45 cu.cm 3 Volume of a sphere = 1 πR³ 3 = 4 π × 5 × 5 × 5 3 ∴ Required number of spheres = 1 π × 30 × 30 × 45 = 81 3 4 π × 5 × 5 × 5 3
- The radius of a metallic cylinder is 3 cm and its height is 5 cm. It is melted and moulded into small cones, each of height 1 cm and base radius 1 mm. The number of such cones formed,is
-
View Hint View Answer Discuss in Forum
Volume of cylinder = πr²h = π × 9 × 5 = 45π cu.cm.
Volume of a cone = 1 πr²h 3 = 1 × π × 1 × 1 3 100 = π cu.cm 300 ∴ Number of cones = 45π = 13500 π 300 Correct Option: D
Volume of cylinder = πr²h = π × 9 × 5 = 45π cu.cm.
Volume of a cone = 1 πr²h 3 = 1 × π × 1 × 1 3 100 = π cu.cm 300 ∴ Number of cones = 45π = 13500 π 300
- The number of spherical bullets that can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being of 4 cm diameter, is (Take π = 22/7)
-
View Hint View Answer Discuss in Forum
Volume of the solid cube = (44 × 44 × 44) cu.cm.
Volume of a bullet = 4 πr³ 3 = 
4 × 22 × 2 × 2 × 2 
cu.cm. 3 7 ∴ Number of bullets = 44 × 44 × 44 × 3 × 7 = 2541 4 × 22 × 2 × 2 × 2 Correct Option: A
Volume of the solid cube = (44 × 44 × 44) cu.cm.
Volume of a bullet = 4 πr³ 3 = 4 × 22 × 2 × 2 × 2 cu.cm. 3 7 ∴ Number of bullets = 44 × 44 × 44 × 3 × 7 = 2541 4 × 22 × 2 × 2 × 2
- A cylindrical rod of iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. The number of such spherical balls is
-
View Hint View Answer Discuss in Forum
Let the radius of the base of cylinder be r units.
Height = 8r units
Its volume = πr² × 8r = 8πr³ cu.unitsRadius of sphere = r 2 Volume = 4 π r ³ 3 2 = πr³ cu.unites 6 ∴ Number of spherical balls = 8πr³ × 6 = 48 πr³ Correct Option: D
Let the radius of the base of cylinder be r units.
Height = 8r units
Its volume = πr² × 8r = 8πr³ cu.unitsRadius of sphere = r 2 Volume = 4 π r ³ 3 2 = πr³ cu.unites 6 ∴ Number of spherical balls = 8πr³ × 6 = 48 πr³
