Question

9
.
If the radius of a 1 m long metallic rod (in cylindrical shape) is 3.5 cm then how
many cones of radius 1 cm and height 2.1 cm can be formed by melting down
the rod? answer is 1750​

Answer 1

Given:

The radius of a 1 m long metallic rod (in cylindrical shape) is 3.5 cm

To find:

How many cones of radius 1 cm and height 2.1 cm can be formed by melting down the rod?

Solution:

The dimensions of the cylindrical-shaped metallic rod:

The radius, r = 3.5 cm

The height, h = 1 m = 100 cm

∴ The volume of the cylindrical-shaped metallic rod is,

= Volume of a cylinder

= $\pi r^2 h$

= $\pi (3.5)^2 \times 100$

The dimension of each of the cones:

The radius, r = 1 cm

The height, h = 2.1 cm

∴ The volume of 1 cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (1)^2 (2.1)$

Now,

The required no. of cones formed by melting down the metallic rod is,

= $\frac{Volume \:of\:rod}{Volume\:of\:1 \:cone}$

= $\frac{\pi (3.5)^2 \times 100}{ \frac{1}{3} \pi (1)^2 (2.1)}$

= $\frac{ 3 \times (3.5)^2 \times 100}{ (1)^2 (2.1)}$

= $\frac{3675}{2.1}$

= $\bold{1750}$

Thus, 1750 cones of radius 1 cm and height 2.1 cm can be formed by melting down the metallic rod.

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A solid metallic rod 15cm long with a diameter of 3.5 cm is melted and made into a rod with a radius of 3.5 cm. What Will be the length of the rod?

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