CUET UG 2025 — General Test Geometry

The lateral surface area of a cylinder is the curved surface, excluding the top and bottom circles.

For a cylinder with radius $r$r and height $h$h:

Lateral surface area $= 2\pi rh$=2πrh

Match: (A) → (III)

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A hemisphere is half of a sphere. The total surface area includes the curved dome and the flat circular base.

Curved surface area $= 2\pi r^2$=2πr2

Flat circular base $= \pi r^2$=πr2

Total surface area $= 2\pi r^2 + \pi r^2$=2πr2+πr2

$$= 3\pi r^2$$=3πr2

Match: (B) → (IV)

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The lateral surface area of a cone is the slanted curved surface, excluding the base.

The slant height from the tip to the edge of the base $= \sqrt{r^2 + h^2}$=r2+h2​

Lateral surface area $= \pi r \times \text{slant height}$=πr×slant height

$$= \pi r\sqrt{r^2 + h^2}$$=πrr2+h2​

Match: (C) → (I)

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The surface area of a sphere with radius $r$r:

Surface area $= 4\pi r^2$=4πr2

Match: (D) → (II)

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Final matching:

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)