Question

plzzz do it #no spam​

Answer 1

${ \bold { \underline{\large{Given : - }}}} \:$

$\tt\star\:{Metallic\:spheres\:of\:radius\:6cm\:,\:8cm\:,\:10cm.}$

$\tt\star\:{They\:are\:melted\:to\:form\:a\:single\:solid\:sphere.}$

${ \bold { \underline{\large{To \: Find : - }}}} \:$

$\tt\star\:{Area\:of\:resulting\:sphere.}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large\boxed{\boxed{\sf{So\:let's \:do\:it\:!}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${ \bold { \underline{ Formula\:that\:we\:will\:use : - }}} \:$

$\tt{Volume_{(Sphere)}\:\leadsto\:\dfrac{4}{3}\pi r^3}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${ \bold { \underline{\large{ Solution : - }}}} \:$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\:{ \bold { \underline{Volume\:of\:sphere\:of\:radius\:6cm : - }}} \:$

$\longmapsto$ $\tt{\dfrac{4}{3}\pi r^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:(6)^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:6\:\times\:6\:\times\:6}$

$\longmapsto$ $\boxed{\tt{\dfrac{19008}{21}}}$ $\red\leadsto$ $\tt\red{(1)}$

$\boxed {\frak {\therefore \pink {Volume\:of\:sphere\:of\:radius\:6cm\:\leadsto\:\dfrac{19008}{21}cm^3}}}\:\red\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\:{ \bold { \underline{Volume\:of\:sphere\:of\:radius\:8cm : - }}} \:$

$\longmapsto$ $\tt{\dfrac{4}{3}\pi r^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:(8)^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:8\:\times\:8\:\times\:8}$

$\longmapsto$ $\boxed{\tt{\dfrac{45056}{21}}}$ $\red\leadsto$ $\tt\red{(2)}$

$\boxed {\frak {\therefore \green {Volume\:of\:sphere\:of\:radius\:8cm\:\leadsto\:\dfrac{45056}{21}cm^3}}}\:\red\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\:{ \bold { \underline{Volume\:of\:sphere\:of\:radius\:10cm : - }}} \:$

$\longmapsto$ $\tt{\dfrac{4}{3}\pi r^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:(10)^3}$

$\longmapsto$ $\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7} \:\times\:10\:\times\:10\:\times\:10}$

$\longmapsto$ $\boxed{\tt{\dfrac{88000}{21}}}$ $\red\leadsto$ $\tt\red{(3)}$

$\boxed {\frak {\therefore \blue {Volume\:of\:sphere\:of\:radius\:10cm\:\leadsto\:\dfrac{88000}{21}cm^3}}}\:\red\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\:{ \bold { \underline{Adding\:\red{(1)}\:,\:\red{(2)}\:and\:\red{(3)} : - }}} \:$

$\longmapsto$ $\tt{\dfrac{19008}{21}\:+\:\dfrac{45056}{21}\:+\:\dfrac{88000}{21}}$

$\longmapsto$ $\tt{\dfrac{19008\:+\:45056\:+\:88000}{21}}$

$\longmapsto$ $\tt{\dfrac{152064}{21}}$ $\red\leadsto$ $\tt\red{(4)}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

ωe know that big sphere is maded by melting the small spheres.

∴Volume of big sphere = Sum of volumes of small spheres.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\therefore$ $\tt \orange {Volume\:of\:big\:sphere\:\leadsto\:\red{(4)}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\tt \underline \purple{So,\:let's \:put\:values\::-}$

ㅤ$\tt{\dfrac{4}{3}\pi r^3\:=\:\dfrac{152064}{21}}$

ㅤ$\tt{\dfrac{4}{3}\:\times\:\dfrac{22}{7}\:\times\:r^3\:=\:\dfrac{152064}{21}}$

ㅤ$\tt{\dfrac{88}{21}\:\times\:r^3\:=\:\dfrac{152064}{21}}$

ㅤ$\tt{r^3\:=\:\dfrac{152064}{21}\:\times\:\dfrac{21}{88}}$

ㅤ$\tt{r^3\:=\:\dfrac{\cancel{152064}}{\cancel{21}}\:\times\:\dfrac{\cancel{21}}{\cancel{88}}}$

ㅤ$\tt{r^3\:=\:1728}$

ㅤ$\tt{r\:=\:\sqrt[3]{1728}}$

ㅤ$\tt{r\:=\:\sqrt[3]{2\:\times\:2\:\times\:2\:\times\:6\:\times\:6\:\times\:6}}$

ㅤ$\tt{r\:=\:2\:\times\:6}$

ㅤ$\boxed{\tt{r\:=\:12}}$

$\boxed {\frak {\therefore \orange {Radius\:of\:resulting\:sphere\:\leadsto\:12cm}}}\:\red\bigstar$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${ \bold { \underline{\large\red{Note : - }}}} \:$

•Dear user , if u are site (brainly.in) user. Then answer will be correctly displayed to you.

•But if you uses the app, please swipe right of the screen to see the full answer.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

ANSWER

Let the radius of the resulting sphere be r cm.

Then, the volume of the resulting sphere = Sum of the volumes of three sphere of radii 6cm,8cm and 10cm

⇒

3

4

πr

3

=

3

4

π×6

3

+

3

4

π×8

3

+

3

4

π×10

3

⇒r

3

=216+512+1000

⇒r

3

=1728

⇒r

3

=12

3

⇒r=12cm