Question

A lead bar 10 cm*5cm*4 cm is melted and made into 5 equal spectacle bullets. find the diameter and surface area of bullet​

Answer 1

Given:

A lead bar 10 cm*5cm*4 cm is melted and made into 5 equal spherical bullets.

To find:

The diameter and surface area of the bullet​

Solution:

The dimensions of the lead bar:

Length = 10 cm

Breadth = 5 cm

Height = 4 cm

∴ The volume of the cuboidal lead bar is,

= length × breadth × height

= 10 × 5 × 4

= 200 cm³

We have, The lead bar is melted and made into 5 spherical bullets

So, Volume of lead bar = 5 × Volume of 1 spherical bullet

⇒ $200 = 5 \times \frac{4}{3} \pi r^3$

⇒ $40 = \frac{4}{3}\times \frac{22}{7} r^3$

⇒ $r^3 = \frac{40 \times 3\times 7}{4 \times 22}$

⇒ $r^3 = 9.5$

⇒ $r = 2.1\:cm$

Now,

∴ Diameter of the sphere = 2r = 2 × 2.1 = 4.2 cm

and

∴ The surface area of the sphere is,

= $4 \pi r^2 = 4 \times \frac{22}{7} \times 2.1^2 = 4 \times 22 \times 0.63 = 55.44 \:cm^2$

Thus,

$\boxed{\bold{Diameter\:of\:the \:sphere \:is\:\rightarrow 4.2\:cm}}$

$\boxed{\bold{Surface \:area \:of\:the \:sphere \:is\:\rightarrow 55.44\:cm^2}}$

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