Question

If a ball having volume 400c.cm.find the area

Answer 1

$\mathfrak{Answer:}$

= 263 cm².

$\mathfrak{Step-by-Step\;Explanation:}$

$\underline{\bold{Given\;in\;the\;Question:}}$

• Volume of the ball = 400 cm³.

$\mathbb{SOLUTION:}$

Let the radius of the ball be r cm .

$\bigstar\quad\textbf{We know that : \boxed{\bold{Volume\;of\;Sphere=\dfrac{4}{3}\pi\:r^3}}}\\\\\\\mathfrak{According\;to\;question:}\\\\\\\implies\tt{\dfrac{4}{3}\pi\;r^3=400}\\\\\\\implies\tt{\pi\;r^3=\dfrac{400\times 3}{4}}\\\\\\\implies\tt{\pi\;r^3=300}\\\\\\\implies\tt{r^3=\dfrac{300}{\pi}}\\\\\\\implies\tt{r^3=95.454546}\\\\\\\implies\tt{r=\sqrt[3]{95.45454546}}\\\\\\\implies\tt{r=4.57.}$

$\bigstar\quad\textbf{We also know that : \boxed{\bold{Total\;surface\;area=4\pi\;r^2}}}\\\\\\\tt{=4\times\dfrac{22}{7}\times (4.57)^2}\\\\\\\tt{=\dfrac{88}{7}\times 20.8849}\\\\\\\tt{=\dfrac{1837.8712}{7}}\\\\\\\tt{=262.5530286\sim 263.}$

$\\\\\boxed{\boxed{\bold{Total\;Surface\;area=263\;cm^2.}}}$

Answer 2

$\underline{\bold{Given:}}$

● Volume of a ball = 400${cm}^{3}$

$\underline{\bold{To\:Find:}}$

● Total surface area.

First of all let find the radius of a ball.

$\bold{We\:know\:that}$

$\boxed{\bold{Volume =\dfrac{4}{3} \pi {r}^{3}}}$

$\implies\bold{\dfrac{4}{3} \pi {r}^{3} = 400{cm}^{3}}$

$\implies\bold{\pi {r}^{3} = 300{cm}^{3}}$

$\implies\bold{{r}^{3} = 4.57{cm}^{3}}$

$\implies\bold{r =\sqrt[3]{\dfrac{1050}{11}}}$

$\implies\bold{r = 4.57cm}$

$\bold{We\:know\:that}$

$\boxed{\bold{TSA = 4 \pi {r}^{2}}}$

$\bold{According\:to\:the\:question}$

$\implies\bold{4 \pi {(4.57)}^{2}}$

$\implies\bold{262.55{cm}^{2}}$

$\boxed{\bold{Total\:Surface\:Area=262.55{cm}^{2}}}$