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 centimetre cube

Answer 1

$\huge\underline\mathbb{SOLUTION:-}$

Answer:

• Mass of the volume = 199697.45 Gram.

Given:

• Diameter of metallic ball = 35 Cm
• Radius of metallic ball = $\mathsf {\frac{35}{2} }$ = 17.5 Cm
• Density of ball = 8.9 gram/cm³

Need To Find:

• Mass of the ball = ?

Explanation:

$\underline \mathsf \blue {Formula\:used\:here\: :-}$

$\implies \mathsf {Volume\:of\:sphere = \frac{4}{3}\pi r^3}$

$\implies \mathsf {Density = \frac{Mass}{Volume}}$

Now, Calculate the volume of sphere.

$\implies \mathsf {Volume\:of\:sphere = \frac{4}{3}\pi r^3}$

$\implies \mathsf {Volume\:of\:sphere = \frac{4}{3}\times 3.14\times 17.5\times 17.5}$

$\implies \mathsf {Volume\:of\:sphere = \frac{67313.75}{3} }$

• Volume of sphere = 22437.91 Cm³.

Now, We know that:

$\implies \mathsf {Density = \frac{Mass}{Volume}}$

$\implies \mathsf {8.9 = \frac{Mass}{22437.91}}$

$\implies \mathsf {Mass = 199697.45\:gram\:(Approx)}$

• Hence,mass of the volume = 199697.45 Gram.

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

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 centimetre cube

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• Density of metallic ball = 8.9 gm/cm³
• Diameter of metallic ball = 35 cm

Or,

• Radius of metallic ball = 35/2 = 17.5 cm

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Mass of metallic ball

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Here, we can say that ,

Volume of Ball = Volume of sphere

we know,

$\small\boxed{\sf{\pink{\:Volume_{Ball}\:=\:\dfrac{4\times \pi\times (radius_{Ball})^3}{3}}}} \\ \\ \small\sf{\:\:\:\:\:\:\:\:(keep\:value\:of\:radius)} \\ \\ \mapsto\sf{\:Volume_{Ball}\:=\:\dfrac{4\times \dfrac{22}{7}\times 17.5^3}{3}} \\ \\ \mapsto\sf{\:Volume_{Ball}\:=\:\dfrac{471625}{21}} \\ \\ \small\boxed{\mathfrak{\bf{\pink{\:Volume_{Ball}\:=\:22458.66\:cm^3}}}}$

Again,

$\small\boxed{\sf{\pink{\:Mass_{Ball}\:=\:Density\times Volume_{Ball}}}} \\ \\ \small\sf{\:(keep\:value\:of\:Density\:and\:Volume\:of\:Ball)} \\ \\ \mapsto\sf{\:Mass_{Ball}\:=\:8.9\times 22458.66} \\ \\ \small\boxed{\mathfrak{\bf{\pink{\:Mass_{Ball}\:=\:199879.17\:gm\:\:\:\:\:\:Ans}}}}$

$\Large{\underline{\mathfrak{\bf{Thus}}}}$

• Mass of metallic ball = 1,99,879.17 gm