Mathematics
Assertion (A) : Three solid silver cubes of side 6 cm, 8 cm and 10 cm are melted and recasted into a single solid cube. The side of the new cube = 2 times the side of the smallest cube.
Reason (R) : Volume of cuboid = (l x b x h) cubic units.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Surface Area, Volume, Capacity
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Answer
When three solid cubes with edges 6 cm, 8 cm, and 10 cm are melted and recast into a single cube, the total volume is the sum of the individual volumes:
Volume of the 6 cm cube : 63 = 216 cm3
Volume of the 8 cm cube : 83 = 512 cm3
Volume of the 10 cm cube : 103 = 1000 cm3
Total volume = 216 + 512 + 1000 = 1728 cm3
Let x cm be the side of new cube formed.
⇒ x3 = 1728 cm3
⇒ x = cm
⇒ x = 12 cm
⇒ x = 2 x 6 cm
⇒ x = 2 x side of the smallest cube melted
So, assertion (A) is true.
When l, b and h represent the length, breadth, and height, respectively of the cuboid.
Volume of cuboid = (l x b x h) cubic units.
So, reason (R) is true.
∴ Both A and R are correct, and R is not the correct explanation for A.
Hence, option 2 is the correct option.
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Related Questions
Statement 1: The volume of a right circular cylinder = Area of cross section (area of circle) x Distance between two circular parallel ends.
Statement 2: Lateral surface area of a closed cylinder is 2πr(r + h) cubic units.
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Both A and R are correct, and R is the correct explanation for A.
Both A and R are incorrect.
A is true, but R is false.
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