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Some small cubes of same height 7 cm but variable length and width are put inside a large cuboid of height 21 cm. Length and width of cuboid is 32 cm and 24 cm, respectively. Small cubes are put such that cubes at the bottom most layer is of similar base area; second layer contains all the cubes of similar base area and third layer have all the cubes of similar base area. Which of the following statement(s) given below is / are TRUE? A: If side of each small cubes at bottom most layer is 8 cm, then maximum number of small cubes that can be put at bottom most layer is 12. B: If maximum of 48 cubes can be put at second layer, then side of each cube at second layer is 6 cm. C: If side of each small cubes at third layer is 1.6 cm, then maximum number of small cubes that can be put at third layer is 300.

Some small cubes of same height 7 cm but variable length and width are put inside a large cuboid of height 21 cm. Length and width of cuboid is 32 cm and 24 cm, respectively. Small cubes are put such that cubes at the bottom most layer is of similar base area; second layer contains all the cubes of similar base area and third layer have all the cubes of similar base area. Which of the following statement(s) given below is / are TRUE? A: If side of each small cubes at bottom most layer is 8 cm, then maximum number of small cubes that can be put at bottom most layer is 12. B: If maximum of 48 cubes can be put at second layer, then side of each cube at second layer is 6 cm. C: If side of each small cubes at third layer is 1.6 cm, then maximum number of small cubes that can be put at third layer is 300. Correct Answer A and C

GIVEN:

Three statements.

CONCEPT:

Mensuration

FORMULA USED:

Volume of cuboid = LBH

Volume of cube = S2

CALCULATION:

A:

Maximum number of small cubes that can be put at bottom most layer = Base area of large cuboid / Base area of one small cube

= (32 × 24) / 82

= 4 × 3

= 12

B:

Maximum number of small cubes that can be put at second layer = Base area of large cuboid / Base area of one small cube

48 = (32 × 24) / a2

⇒ a2 = 16

⇒ a = 4

Side of each small cube = a = 4 cm

C:

Maximum number of small cubes that can be put at third layer = Base area of large cuboid / Base area of one small cube

= (32 × 24) / 1.62

= 20 × 15

= 300

Hence, only statements A and C are TRUE. 

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