Question

10. How many spheres 12 cm in diameter can be made from a metallic
cylinder of diameter 8 cm and height 90 cm?​

Answer 1

Answer:

5

Step-by-step explanation:

R1 =12/2=6cm

R2=8/2=4cm

H=90 cm

Volume of sphere =4/3*π*R1^3=288π

Volume of cylinder =π*r2^2*h= 1440π

N=volume of cylinder / Volume of Sphere

=1440π/288π = 5

please mark me as the brainliest answer

Answer 2

AnswEr:

$\star\;{\underline{\purple{\sf{As\;per\;GivEn\;QuesTion\;:}}}}$

☯ A metallic cylinder is melted to form spheres.

$\normalsize\;\;\bullet\;\sf Diameter\;of\;Spheres\;:\; \bf{12\;cm}$

$\normalsize\;\;\bullet\;\sf Radius\;of\;Spheres\;:\; \bf{6\;cm}$

$\normalsize\;\;\bullet\;\sf Diameter\;of\;a\; metallic\; cylinder\;:\; \bf{8\;cm}$

$\normalsize\;\;\bullet\;\sf Radius\;of\;a\; metallic\; cylinder\;:\; \bf{4\;cm}$

$\normalsize\;\;\bullet\;\sf Height\;of\;a\; metallic\; cylinder\;:\; \bf{90\;cm}$

$\rule{170}{2}$

$\underline{\bigstar\:\textsf{Lets\;head\;to\;the\; QueStion\;now:}}$

GivEn that,

$\normalsize\;\;\bullet\;\sf Radius\;of\;Spheres\;:\; \bf{6\;cm}$

Therefore,

$\maltese\;{\boxed{\sf{Volume\;of\;sphere\;: \dfrac{4}{3} \pi r^3}}}\\\\:\implies\sf \dfrac{4}{ \cancel{3}} \times \dfrac{22}{7} \times \cancel{6} \times 6 \times 6\\\\:\implies\sf 4 \times \dfrac{22}{7} \times 2 \times 6 \times 6\\\\:\implies\sf 288 \times \dfrac{22}{7}\\\\:\implies\sf \red{ \dfrac{6336}{7}\;cm^3}\;\bigstar$

Now we have,

$\normalsize\;\;\bullet\;\sf Radius\;of\;a\; metallic\; cylinder\;:\; \bf{4\;cm}$

$\normalsize\;\;\bullet\;\sf Height\;of\;a\; metallic\; cylinder\;:\; \bf{90\;cm}$

Therefore,

$\maltese\;{\boxed{\sf{Volume\;of\;Cylinder\;: \pi r^2 h}}}\\\\:\implies\sf \dfrac{22}{7} \times 4 \times 4 \times 90\\\\:\implies\sf 1440 \times \dfrac{22}{7}\\\\:\implies\sf \red{ \dfrac{31680}{7}\;cm^3}\;\bigstar$

$\rule{170}{2}$

Now,

We have to find, No. of sphere that can be made from a metallic cylinder.

$:\implies\sf \dfrac{ Volume_{(Cylinder)}}{ Volume_{(Sphere)}}\\\\:\implies\sf \dfrac{ \frac{31680}{ \cancel{7}}}{ \frac{6336}{ \cancel{7}}}\\\\:\implies\sf \cancel{ \dfrac{31680}{6336}}\\\\:\implies{\bf{\pink{5\;cm^3}}}\;\bigstar$

$\sf\dag\; \underline{Hence,\;5\;sphere\;can\;be\;formed\;from\;given\;metallic\;sphere.}$