CUET UG 2025 — General Test Geometry

2025mcqmedium

If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.

Official previous-year question

Held on 28 May 2025 · Verified 13 Jul 2026.

Options

A
1 cm
B
0.01 cm
C
0.1 cm
D
0.5 m

Did you get this right?

Solution

When a metal rod is stretched into a wire, the volume remains constant.

Original rod:
Length = 10 cm
Radius = 2 cm

Stretched wire:
Length = 40 m = 4000 cm
Radius = $r$ (to find)

The rod is a cylinder with volume:

Volume = $\pi r^2 h$

Volume = $\pi \times (2)^2 \times 10$

Volume = $\pi \times 4 \times 10$

Volume = $40\pi$ cm³

The stretched wire is also a cylinder with volume:

Volume = $\pi \times r^2 \times 4000$

Since the volume remains constant:

$40\pi = \pi \times r^2 \times 4000$

$40 = r^2 \times 4000$

$r^2 = \dfrac{40}{4000}$

$r^2 = \dfrac{1}{100}$

$r = \dfrac{1}{10}$

$r = 0.1$ cm

Therefore, the radius of the stretched wire is $0.1$ cm.

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Solution

When a metal rod is stretched into a wire, the volume remains constant.

Original rod:
Length = 10 cm
Radius = 2 cm

Stretched wire:
Length = 40 m = 4000 cm
Radius = $r$ (to find)

The rod is a cylinder with volume:

Volume = $\pi r^2 h$

Volume = $\pi \times (2)^2 \times 10$

Volume = $\pi \times 4 \times 10$

Volume = $40\pi$ cm³

The stretched wire is also a cylinder with volume:

Volume = $\pi \times r^2 \times 4000$

Since the volume remains constant:

$40\pi = \pi \times r^2 \times 4000$

$40 = r^2 \times 4000$

$r^2 = \dfrac{40}{4000}$

$r^2 = \dfrac{1}{100}$

$r = \dfrac{1}{10}$

$r = 0.1$ cm

Therefore, the radius of the stretched wire is $0.1$ cm.

CUET UG 2025 — General Test Geometry

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Solution

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry