Question

A lead bar 10cm X 5cm X 4cm is melted and made into 5 equal spherical bullets. Find the diameter and surface area of bullet.​

Answer 1

Given

• Lead bar 10cm × 5cm × 4cm.
• Is mealted Into 5 equal spherical bullets .

To Find

• Find the diameter and surface area of bullet.

Solution

$\sf \: Volume \: Of \: lead \: bar = 10cm × 5cm × 4cm$

$\sf \: Volume \: Of \: lead \: bar = 200cm³$

Now The lead Bar is melted and made into 5 equal spherical bullets.

$\sf \: Volume \: of \: 5 \: spherical \: bullets = 200cm²$

$\sf \: Volume \: of \: 1 \: spherical \: bullets = \frac{ 200cm²}{5}$

$\sf \: Volume \: of \: 1 \: spherical \: bullets = 40 {cm}^{3}$

Now

• We need To Find Diameter of Spherical bullets And then the surface area of bullet.

${\implies \sf \: Volume \: of \: Spherical \: bullets= 40cm³}$

$\implies \sf \: \dfrac{4}{3} \pi {r}^{3} = 40$

$\implies\sf \: {r}^{3} = 40 \times \dfrac{3}{4} \times \dfrac{7}{22}$

$\implies \sf \: {r}^{3} = 9.54$

$\implies \sf \: r = 2.1$

$~~~~~~~~~\pink{\sf Diameter\ Of \ Sphare= 2.1×2=4.2cm}$

Now ,

$\sf \: Surface \: area \: of \: Sphere= 4πr²$

${\implies \sf \: Surface \: area \: of \: Sphere= 4 \times \dfrac{22}{7} \times (2.1)²}$

${\implies \sf \: Surface \: area \: of \: Sphere= 4 \times \dfrac{22}{7} \times 4.41}$

${\implies\sf \: Surface \: area \: of \: Sphere=88 \times 0.60}$

$~~~~~~~~~\green{\sf \: Surface \: area \: of \: Sphere=55.44cm ^{2} }$