Question

A spherical ball is divided into two equal halves. Given that the curved surface area of each half is 56.57 cm, what will be the volume of the spherical ball?

Answer 1

${\large{\pmb{\sf{\underline{About \; question...}}}}}$

❍ A spherical ball is divided into two equal halves. Given that the curved surface area of each half is 56.57 cm², what will be the volume of the spherical ball?

This question says that we have to find out the volume of the spherical ball whose curved surface area is given as 56.57 cm and that spherical ball is divided into two equal halves. Let's do it!

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

❍ Spherical ball is divided into two equal halves.

❍ The curved surface area of the given spherical ball = 56.57 cm

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

❍ Volume of the spherical ball.

${\large{\pmb{\sf{\underline{Solution...}}}}}$

❍ Volume of the spherical ball = 113.04 cm²

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

❍ Formula to find volume of sphere.

❍ Formula to find surface area of sphere.

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

❍ V of sphere = ${\sf{\dfrac{4}{3} \pi r^{3}}}$

❍ Surface area of sphere = ${\sf{2 \pi r^{2}}}$

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Firstly by using this formula i.e., ${\sf{2 \pi r^{2}}}$ let's find the radius of sphere. As we already know π's value is 22/7 or 3.14 We can take it as we want but I prefer π as 3.14 maximum.

$:\implies \sf Area \: = 56.57 \: cm^{2} \\ \\ :\implies \sf 2 \pi r^{2} \: = 56.57 \\ \\ :\implies \sf 2 \times 3.14 \times r^{2} \: = 56.57 \\ \\ :\implies \sf r^{2} \: = 56.57 / 2 \times 3.14 \\ \\ :\implies \sf r^{2} \: = 56.57/6.28 \\ \\ :\implies \sf r^{2} \: = 9 \\ \\ :\implies \sf {r} \: = \sqrt{9} \\ \\ :\implies \sf {r} \: = 3 \: cm$

• Henceforth, 3 cm is the radius of the given spherical ball.

~ Now let's find the volume of the spherical ball by using this formula i.e., ${\sf{\dfrac{4}{3} \pi r^{3}}}$

$:\implies \sf Volume \: = \dfrac{4}{3} \times \pi \times r^{3} \\ \\ :\implies \sf Volume \: = \dfrac{4}{3} \times 3.14 \times 3^{3} \\ \\ :\implies \sf Volume \: = \dfrac{4}{3} \times 3.14 \times 3 \times 3 \times 3 \\ \\ :\implies \sf Volume \: = \dfrac{4}{3} \times 3.14 \times 9 \times 3 \\ \\ :\implies \sf Volume \: = \dfrac{4}{3} \times 3.14 \times 27 \\ \\ :\implies \sf Volume \: = \dfrac{4}{3} \times 84.78 \\ \\ :\implies \sf Volume \: = 113.04 \: cm^{3}$

• Henceforth, volume of the spherical ball is 113.04 cm³

Answer 2

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$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• A spherical ball is divided into two equal halves. Given that the curved surface area of each half is 56.57 cm, what will be the volume of the spherical ball?

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$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\sf{Spherical \: ball \:is \:divided\: into \:2\: equal \:halves.}$

• $\sf{CSA \:of\: each\: half \:= \:56.57\: cm^{2}}$

• $\sf{CSA \:of \:spherical \:ball \:=\: 56.57 \:+ \:56.57\: = \:113.14 \:cm^{2}}$

• $\boxed{\sf{CSA \:of \:sphere \:=\: 4 \pi r^{2} \:units^{2}}}$

• $\sf{113.14 = 4 * \dfrac{22}{7} * r^{2}}$

• $\sf{\dfrac{113.14}{4} = \dfrac{22}{7} * r^{2}}$

• $\sf{\dfrac{28.285}{3.14} = r^{2}}$

• $\sf{9.00 = r^{2}}$

• $\sf{r = \sqrt{9}}$

• $\sf{r = 3 \: cm}$

• $\sf{Volume\: of\: sphere \:=\: \dfrac{4}{3} \pi r^{3} \:units^{2}}$

• $\sf{\dfrac{4}{3} \pi r^{3} \:units^{3}}$

• $\sf{\dfrac{4}{3} * \dfrac{22}{7} * 3^{3}}$

• $\sf{\dfrac{4}{3} * 3.14 * 27}$

• $\sf{\dfrac{4}{3} * 84.78}$

• $\sf{1.33 * 84.78}$

• $\sf{ 112.757\:cm^{3}}$

• $\boxed{\sf{ 113\:cm^{3}}}$

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$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\sf{Volume\: of\: the\: spherical\: ball \:= \:113 \:cm^{3}}}$

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$\huge{\bf{\purple{\mathfrak{Extra \: Information:-}}}}$

• $\sf{CSA \:/ \:TSA \:of \:sphere\: = 4 \pi r^{2} \: units^{2}}$

• $\sf{Volume \:of \:sphere = \:\dfrac{4}{3} \pi r^{3}\: units^{3}}$

• $\sf{CSA\: of \:hemisphere\: = \:2 \pi r^{2}\: units^{2}}$

• $\sf{TSA\: of\: hemisphere\: = \:3 \pi r^{2} \: units{2}}$

• $\sf{Volume \:of \:hemisphere \:=\: \dfrac{2}{3} \pi r^{3} \: units^{3}}$

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$\huge{\bf{\blue{\mathfrak{Note:-}}}}$

• [A spherical ball is divided into two equal halves. Curved surface area of each half is 56.57 cm²]

• This means that the spherical ball is divided into 2 halves and the given CSA of hemisphere is 56.57 cm².

• So, we have to multiply 56.57 cm² with 2 to get the CSA of sphere as sphere is the combination of the divided 2 equal hemispheres.

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