Question

The diameter of metallic ball is 35 cm. What is the mass of the ball if the density of metal is 8.9 gm per centimeter cube?

Answer 1

${\huge{\bf{\underline{\underline{\red{Solution:}}}}}}\\ \\ \\ {\underline{\bf{Given:}}}\\ \\ \leadsto \sf Diameter\;of\;metallic\;ball=35\;cm\\ \\ \leadsto \sf Radius\;of\;metallic\;ball= \dfrac{35}{2}=17.5\;cm\\ \\ \leadsto \sf Density\;of\;ball=8.9\;gm/cm^{3}\\ \\ \\ {\underline{\bf{To\;Find:}}}\\ \\ \leadsto \sf Mass\;of\;the\;ball.\\ \\ \\ {\underline{\bf{Formula\;used:}}}\\ \\ \leadsto \sf Volume\;of\;sphere=\dfrac{4}{3}\pi r^{3}\\ \\ \leadsto \sf Density=\dfrac{Mass}{Volume}\\ \\ \rule{200}{1}$

${\underline{\bf{Now,\;first\;we\;will\;calculate\;volume\;of\;sphere,}}}\\ \\ \leadsto \sf Volume\;of\;sphere=\dfrac{4}{3}\pi r^{3}\\ \\ \\ \leadsto \sf Volume\;of\;sphere=\dfrac{4}{3}\times 3.14\times 17.5\times 17.5\times 17.5\\ \\ \\ \leadsto \sf Volume\;of\;sphere= \dfrac{67313.75}{3}\\ \\ \\ \leadsto {\boxed{\sf Volume\;of\;sphere= 22437.91\;cm^{3}}}\\ \\ \rule{200}{1}$

${\bf{\underline{Now,\;we\;know\;that,}}}\\ \\ \\ \leadsto \sf Density=\dfrac{Mass}{Volume}\\ \\ \\ \leadsto \sf 8.9=\dfrac{Mass}{22437.91}\\ \\ \\ \leadsto \sf Mass = 199697.45\;gm\;(Approx)\\ \\ \\ \leadsto {\boxed{\sf{Hence,\;mass\;of\;the\;ball = 199697.45\;gm}}}$

Answer 2

Question :--- The diameter of metallic ball is 35 cm. What is the mass of the ball if the density of metal is 8.9 gm per centimeter cube ?

Formula used :--

→ Volume of Sphere = 4/3 * π * (r)³ ( where r is radius of sphere , that is Half of diameter ).

→ Mass of the ball = Density of metal * Volume.

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Solution :--

Diameter of sphere is given = 35cm.

So,

→ Radius of sphere = (35/2) cm.

Putting value of radius in Volume formula now,

→ Volume of Sphere = 4/3 * π * (r)³

→ Volume = 4/3 * π * (35/2) ³

→ Volume = (4/3) * (22/7) * (35/2) * (35/2) * (35/2)

→ Volume = (11 * 35 * 35 * 35) /3*7

→ Volume = (471625/21) cm³ .

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Now, it is given that, Density of Metal is 8.9gm /cm³.

And , now we also have Volume of sphere = (471625/21)cm³ .

So,

→ Mass of ball = Density * Volume .

putting values now,

→ Mass of ball = 8.9 * (471625/21)

→ Mass of ball = 199879.17gm.

Now, we know that, ( As SI unit of mass is kg.)

→ 1000gm = 1kg

→ 1gm = (1/1000)kg .

So,

→ 199,879.17gm = (199,879.17)/1000 = 199.879 kg (Approx)

Hence, Mass of the Metallic ball is 199.879kg .