CUET UG 2025 — General Test Geometry

For a cube with side length $a$a, the body diagonal is $a\sqrt{3}$a3​.

Given diagonal $= 6\sqrt{3}$=63​ cm:

$$a\sqrt{3} = 6\sqrt{3}$$a3​=63​

$a = 6$a=6 cm

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Volume of cube $= a^3$=a3

Volume $= 6^3$=63

Volume $= 216$=216 cm³

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Surface area of cube $= 6a^2$=6a2

Surface area $= 6 \times 6^2$=6×62

Surface area $= 6 \times 36$=6×36

Surface area $= 216$=216 cm²

Volume and surface area are numerically equal.

Statement (A) is true.

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To cut the block into equal cubes, the side of each cube must divide all three dimensions.

The largest such cube has side $= \text{GCD}(6, 12, 15)$=GCD(6,12,15)

$$6 = 2 \times 3$$6=2×3

$$12 = 2^2 \times 3$$12=22×3

$$15 = 3 \times 5$$15=3×5

$\text{GCD} = 3$GCD=3 cm

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Number of cubes $= \dfrac{6}{3} \times \dfrac{12}{3} \times \dfrac{15}{3}$=36​×312​×315​

Number of cubes $= 2 \times 4 \times 5$=2×4×5

Number of cubes $= 40$=40

The minimum number of cubes is 40, not 27.

Statement (B) is false.

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Only statement (A) is true.