CUET UG 2025 — General Test Geometry

The tent is conical in shape and requires cloth to cover the curved surface area (the slanted outer surface, excluding the base).

Given:

• Radius of tent base: $r = 21$r=21 m
• Height of tent: $h = 20$h=20 m
• Width of cloth available $= 6$=6 m

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The slant height is needed since the cloth wraps around the slanted side.

Using Pythagoras theorem:

$$l = \sqrt{r^2 + h^2}$$l=r2+h2​

$$l = \sqrt{21^2 + 20^2}$$l=212+202​

$$l = \sqrt{441 + 400}$$l=441+400​

$$l = \sqrt{841}$$l=841​

$l = 29$l=29 m

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The curved surface area of the cone:

Curved Surface Area $= \pi r l$=πrl

$$= \frac{22}{7} \times 21 \times 29$$=722​×21×29

$$= 22 \times 3 \times 29$$=22×3×29

$$= 66 \times 29$$=66×29

$= 1914$=1914 m²

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The cloth comes in a roll that is $6$6 m wide. The length of cloth required:

Length $= \frac{\text{Area}}{\text{Width}}$=WidthArea​

Length $= \frac{1914}{6}$=61914​

Length $= 319$=319 metres

Therefore, $319$319 metres of cloth is required.