Question

the diameter of a metallic ball is 35 CM what is the mass of the ball if the density of the metal is 8.9 gm per cm cube​

Answer 1

S O L U T I O N

$\frak{Given}\begin{cases}\sf { \: \: \: \: Diameter \;of\;Ball = 35\;cm}\ \\\sf{\:\; \: \; Radius = \dfrac{Diameter}{2} = \cancel\dfrac{35}{2} = 17.5\;cm}\\\sf{\:\;\; \: Density \;of\;metal = 8.9 gm/cm^3}\end{cases}$

To find: Mass of the Ball?

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\star\;\boxed{\sf{\pink{Volume_{sphere} = \dfrac{4}{3} \pi r^3}}}$

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$:\implies\sf Volume_{sphere} = \dfrac{4}{3} \times \dfrac{22}{7} \times (17.5) \times (17.5) \times (17.5) \\\\\\:\implies\sf Volume_{sphere} = \cancel\dfrac{67313.75}{3} \\\\\\:\implies{\underline{\boxed{\sf{ Volume_{sphere} = 22437.91\;cm^3}}}}$

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$\star\;\boxed{\sf{\pink{Density = \dfrac{Mass}{Volume}}}}$

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$\underline{\bf{\dag} \:\mathfrak{Substituting\;values\: :}}$⠀

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$:\implies \mathsf {8.9 = \frac{Mass}{22437.91}} \\\\\\\:\implies \sf Mass = 22437.91 \times 8.9\\\\\\:\implies{\underline{\boxed{\sf{\pink{Mass = 199697.45}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; required\;mass\;is\; \bf{ 199697.45\;(approx)}.}}}$

Answer 2

Answer:

Given:-

• Diameter of metlic ball = 35cm
• Radius of metlic ball = $\frac{35}{2}$= 17.5cm
• Density of Ball = 8.9gm

To Find:-

• Mass of the ball

Formula used:-

• Volume of sphere = $\Large\frac{4}{3}$πr³
• Density = $\Large\frac{mass}{volume}$

According to Question:-

Volume of Sphere = $\Large\frac{4}{3}$πr³

Volume of Sphere = $\Large\frac{4}{3} \times 3.14 \times 17.5 \times 17.5$= 67313.65

Volume of Sphere = ${\cancel{\dfrac{67313.65}{3}}}$= 22436.91 cm³

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Density = $\Large\frac{mass}{volume}$

8.9 = $\Large\frac{mass}{22437.91}$

Mass = 199697.45 g

Hence, Mass of the volume = 199697.45 Gram.