Mensuration
- A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cubic cm) is
-
View Hint View Answer Discuss in Forum
The external dimensions of the box are : Length = 20 cm,
Breadth = 12cm,
Height = 10 cm
External volume of the box = 20 × 12 × 10 = 2400 cm³.
Thickness of the wood = 1 cm Internal length = 20 – 2 = 18 cm
∴ Internal breadth = 12 – 2 = 10 cm
Internal height = 10 – 2 = 8 cm
Internal volume = 18 × 10 × 8 = 1440 cm³.
Volume of the wood = (2400 – 1440) cm³ = 960 cm³.Correct Option: A
The external dimensions of the box are : Length = 20 cm,
Breadth = 12cm,
Height = 10 cm
External volume of the box = 20 × 12 × 10 = 2400 cm³.
Thickness of the wood = 1 cm Internal length = 20 – 2 = 18 cm
∴ Internal breadth = 12 – 2 = 10 cm
Internal height = 10 – 2 = 8 cm
Internal volume = 18 × 10 × 8 = 1440 cm³.
Volume of the wood = (2400 – 1440) cm³ = 960 cm³.
- The area of three adjacent faces of a cuboid are x, y, z square units respectively. If the volume of the cuboid be y cubic units, then the correct relation between v, x, y, z is
-
View Hint View Answer Discuss in Forum
If l, b, h be the dimensions of the cuboid, then volume of the cuboid = l × b × h
Now, x = l × b, y = l × h,
z = b × h
∴ xyz = l² × b² × h² = v²Correct Option: A
If l, b, h be the dimensions of the cuboid, then volume of the cuboid = l × b × h
Now, x = l × b, y = l × h,
z = b × h
∴ xyz = l² × b² × h² = v²
- Water flows into a tank which is 200m long and 150m wide, through a pipe of cross-section 0.3m × 0.2m at 20 km/hour. Then the time (in hours) for the water level in the tank to reach 8m is
-
View Hint View Answer Discuss in Forum
Water supplied by pipe in 1 hour = (0.3 × 0.2 × 20 × 1000) cubic metre
= 1200 cubic metre∴ Total time = Volume of water to be filled in the tank 1200 = 200 × 150 × 8 = 200 hours 1200 Correct Option: D
Water supplied by pipe in 1 hour = (0.3 × 0.2 × 20 × 1000) cubic metre
= 1200 cubic metre∴ Total time = Volume of water to be filled in the tank 1200 = 200 × 150 × 8 = 200 hours 1200
- A rectangular sheet of metal is 40cm by 15cm. Equal squares of side 4cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is
-
View Hint View Answer Discuss in Forum
Length of the box = 40 – 2 × 4 = 32 cm
Breadth of the box = 15 – 2 × 4 = 7 cm
Height of the box = 4 cm
∴ Volume of the box = 32 × 7 × 4 = 896 cu. cm.Correct Option: A
Length of the box = 40 – 2 × 4 = 32 cm
Breadth of the box = 15 – 2 × 4 = 7 cm
Height of the box = 4 cm
∴ Volume of the box = 32 × 7 × 4 = 896 cu. cm.
- The areas of three consecutive faces of a cuboid are 12 cm², 20 cm² and 15 cm2, then the volume (in cm³) of the cuboid is
-
View Hint View Answer Discuss in Forum
Let the length, breadth and height of the cuboid be x, y and z cm respectively, then
xy = 12 ; yz = 20 ; zx = 15
∴ x²y²z² = 12 × 20 × 15 = 3600 cm6
∴ v = xyz = √3600 = 60cm³Correct Option: D
Let the length, breadth and height of the cuboid be x, y and z cm respectively, then
xy = 12 ; yz = 20 ; zx = 15
∴ x²y²z² = 12 × 20 × 15 = 3600 cm6
∴ v = xyz = √3600 = 60cm³
