Question

the number of lead balls of diamater 1 cm each that can be made from a sphere of diameter 16 cm is

Answer 1

Given:

• Diameter of lead balls = 1cm
• Diameter of Sphere = 16cm

Find:

• No. of lead balls can made

Solution:

we, know that

$\boxed{\rm Volume \: of \: sphere = 4 \pi {r}^{3}}$

where,

• π = 22/7
• r = D/2 = 16/2 = 8cm

So,

$\dashrightarrow\rm Volume \: of \: sphere = 4 \pi {r}^{3}$

$\dashrightarrow\rm Volume \: of \: sphere = 4 \times \dfrac{22}{7} \times {(16)}^{3}$

$\dashrightarrow\rm Volume \: of \: sphere = 4 \times \dfrac{22}{7} \times 4096$

$\dashrightarrow\rm Volume \: of \: sphere = \dfrac{360448}{7}$

$\dashrightarrow\rm Volume \: of \: sphere = \dfrac{360448}{7} {cm}^{3}$

Now,

$\boxed{\rm Volume \: of \: lead \: ball= 4 \pi {r}^{3}}$

where,

• π = 22/7
• r = D/2 = 1/2cm

So,

$\dashrightarrow\rm Volume \: of \: lead \: ball= 4 \pi {r}^{3}$

$\dashrightarrow\rm Volume \: of \: lead \: ball= 4 \times \dfrac{22}{7} \times { \bigg(\dfrac{1}{2} \bigg)}^{3}$

$\dashrightarrow\rm Volume \: of \: lead \: ball= 4 \times \dfrac{22}{7} \times \dfrac{1}{8}$

$\dashrightarrow\rm Volume \: of \: lead \: ball= \dfrac{88}{56}$

$\dashrightarrow\rm Volume \: of \: lead \: ball= \dfrac{88}{56} {cm}^{3}$

Now,

$\rm\to No. \: of \: lead \: balls = \dfrac{volume \: of \: sphere}{volume \: of \: lead \: balls}$

$\rm\to No. \: of \: lead \: balls = \dfrac{\dfrac{360448}{7} }{\dfrac{88}{56} }$

$\rm\to No. \: of \: lead \: balls = \dfrac{360448}{7} \times \dfrac{56}{88}$

$\rm\to No. \: of \: lead \: balls = \dfrac{20185088}{616}$

$\rm\to No. \: of \: lead \: balls = 32768$

$\rm\therefore No. \: of \: lead \: balls = 32768$

So, 32768 balls can be made from given sphere