CUET UG 2025 — General Test Geometry

The curved surface area (CSA) of a cone is given by:

$$\text{CSA} = \pi r l$$CSA=πrl

where $r$r is the radius of the base and $l$l is the slant height.

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Let the original radius be $r$r and the original slant height be $l$l.

Original CSA $= \pi r l$=πrl

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The slant height decreases by 15%, so the new slant height is 85% of the original:

New slant height $= 0.85l$=0.85l

The radius increases by 20%, so the new radius is 120% of the original:

New radius $= 1.20r$=1.20r

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The new curved surface area is:

New CSA $= \pi \times (1.20r) \times (0.85l)$=π×(1.20r)×(0.85l)

New CSA $= \pi \times 1.20 \times 0.85 \times r \times l$=π×1.20×0.85×r×l

New CSA $= 1.02 \times \pi r l$=1.02×πrl

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The new CSA is 1.02 times the original CSA, which represents 102% of the original.

Percentage change $= (1.02 - 1) \times 100\%$=(1.02−1)×100%

Percentage change $= 0.02 \times 100\%$=0.02×100%

Percentage change $= 2\%$=2%

Since the new CSA is greater than the original, this represents a 2 percent increase.