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4

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A. 20

B. 30

C. 40

D. 50

Correct Answer :

C. 40


      Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3.


       Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.


       Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3.


       Number of cubes = 1080/27 = 40.

Related Questions

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A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

A. 20

B. 30

C. 40

D. 50

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A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20 cm x 15 cm, find the rise in water level.

A. 10 cm

B. 10.25 cm

C. 11 cm

D. 11.25 cm

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Water flows into a tank 200 m x 160 m througb a rectangular pipe of 1.5m x 1.25 m @  20 kmph . In what time (in minutes) will the water rise by metres?

A. 50 min

B. 55 min

C. 90 min

D. 96 min

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How many iron rods, each of length 7 m and diameter 2 cm can be made out of 0.88 cubic meter of iron?

A. 200

B. 330

C. 400

D. 450

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A conical vessel, whose internal radius is 12 cm and height 50 cm, is full of liquid. The contents are emptied into a cylindrical vessel with internal radius 10 cm. Find the eight to which the liquid rises in the cylindrical vessel.

A. 20 cm

B. 21 cm

C. 23 cm

D. 24 cm

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Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.        


 

A. 1:2

B. 2:3

C. 2:5

D. 1:9

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The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

A. 8 kg

B. 8.04 kg

C. 8.5 kg

D. 8.004 kg

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Find the number of bricks, each measuring 24 cm x 12 cm x 8 cm, required to construct a wall 24 m long, 8m high and 60 cm thick, if 10% of the wall is filled with mortar?

A. 40,000

B. 42,000

C. 45,000

D. 47,000

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The surface area of a cube is 1734 sq. cm. Find its volume.

A. 4012 cm3

B. 4711 cm3.

C. 4812 cm3.

D. 4913 cm3.

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Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new Cube. Find the surface area of the cube so formed.

A. 486 cm2.

B. 488cm2.

C. 479 cm2.

D. 445 cm2.

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The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

A. 30 cm

B. 40 cm

C. 50 cm

D. 55 cm

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Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m high.

A. 345 cm2

B. 868 cm2

C. 876 cm2

D. 678 cm2