Geometry

Solids

Medium

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.

1 cm

0.01 cm

0.1 cm

0.5 m

✅ Correct Option: 3

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.

2025: 26 May Shift 1

A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere is:

2025: 15 May Shift 1

$V_1, V_2, V_3$ and $V_4$ are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respectively. The following statements regarding these volumes are given below.

(A) $V_1 + V_2 + 2V_3 < V_4$

(B) $V_1 + 3V_2 > V_3 + V_4$

(D) $V_1 + 4V_2 + V_3 < V_4$

Which of these statements is/are correct?

Choose the correct answer from the options given below:

2025: 3 June Shift 2

A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively.

What is the volume of clay required for making a tile?

2026: 18 May Shift 1

Consider the surface areas of the following solids.

(A) A cuboid of 12 cm long, 7 cm broad, and 5 cm high.

(B) A cylinder of radius 3.5 cm and height 60 cm.

(D) A sphere of radius 12.5 cm.

Arrange the above in decreasing order.

2026: 21 May Shift 1

Consider the surface areas of the following solids:

(A) A cuboid of 10 cm long, 7 cm broad, and 5 cm high.

(B) A cylinder of radius 3.5 cm and height 60 cm.

(D) A sphere of radius 12 cm.

Arrange the above in decreasing order.

2026: 14 May Shift 1

If r represent the radius and h denotes the height of the solid. Then, Match List-I with List-II

LIST-I (Solid)	LIST-II (Volume)
A. Cylinder	I. $\dfrac{2}{3}\pi r^3$
B. Cone	II. $\dfrac{4}{3}\pi r^3$
C. Sphere	III. $\dfrac{1}{3}\pi r^2 h$
D. Hemisphere	IV. $\pi r^2 h$

Choose the correct answer from the options given below:

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.

Solution

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