Question

A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm, find the volume of the spherical ball. [use t = 3.14​

Answer 1

Answer:

• 113.04 cm³

Step-by-step explanation:

We know the formula of CSA of hemisphere. (As the spherical ball is divided into two equal halves, it forms a hemisphere)

$\sf \: CSA = 2\pi {r}^{2}$

• r = radius of hemisphere

As given,

$\sf \: 2\pi {r}^{2} = 56.57$

$\implies \sf \: 2 \times 3.14 \times {r}^{2} = 56.57$

$\implies \sf \: {r}^{2} = \dfrac{56.57}{6.28} = 9$

$\sf \: r = \sqrt{9} = 3$

Now, the formula of volume of sphere,

$\sf \: V = \dfrac{4}{3} \pi {r}^{3}$

According to given question,

$\sf \: V = \dfrac{4}{3} \times 3.14 \times {3}^{3}$

$\therefore \sf \: V = 113.04 \: {cm}^{3}$

Answer 2

$\large\underline{\underline{\sf{\maltese\:\: \red{Given :}}}}$

• A spherical ball is divided into two equal parts.

• Curved Surface Area (CSA) of each half = 56.57 cm

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$\large\underline{\underline{\sf{\maltese\:\: \red{To \: Find \: : }}}}$

• Volume of the spherical ball = ?

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$\large\underline{\underline{\sf{\maltese\:\: \red{Concept \: Used \: : }}}}$

• Curved Surface Area (CSA) of Sphere = 2πr²

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$\large\underline{\underline{\sf{\maltese\:\: \red{Solution \: : }}}}$

$\sf 2\pi r^2 = 56.57cm^2$

$\implies 2 \: \times \: 3.14 \: \times \: r^2 = 56.57$

$\implies r^2 = \frac{56.57 }{2 \: \times 3.14}$

$\implies r^2 = 9 \\ \implies r = \sqrt{9}$

$\implies r \approx \bold{3 cm}$

Volume of Sphere = $\frac{4}{3} \pi r^3$

Volume of Sphere = $\frac {4}{3} \: \times \: 3.14 \: \times \: 3 \: \times \: 3 \: \times \: 3$

Volume of Sphere = $\bold{113.04 \: cm^3}$

∴ Volume of the spherical ball is 113.04 cm³.

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$\large\underline{\underline{\sf{\maltese\:\: \red{Additional \: Information \: :}}}}$

Formulas related to Surface Area & Volume :

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$