Question

02.
A sphere has a volume of 850 m³. Find its surface
area.​

Answer 1

Given:

• Volume of sphere = 850 m³.

To Find:

• Surface Area of sphere.

Solution:

As we know that,

★Volume of sphere = 4/3πr³.

⇒850=4/3 × 22/7 × r³

⇒r³ = 850 × 3 × 7 ÷ 4 × 22

⇒r³ = 202.84

⇒r = ³√202.84

⇒r = 5.88 m

★Surface area of sphere = 4πr²

⇒ 4 × 22/7 × 5.88 ×5.88

⇒ ≈ 434m²

Hence,

Surface Area of sphere = 434m²

Answer 2

$\rule{200}4$

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

• $\sf{A\:sphere\:has\:a\:volume\:of\:\bf{850\:m^3}}$

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

• $\sf{Surface\:area\:of\:sphere}$

${ \bold { \underline { \underline{\maltese\:Solution\:\maltese }}}} \:$

$\:\:\:\:\:\:\:\:\:\:\:\: \:\:\:\large\underbrace{\underline{\sf{How\:to\:solve\:it\::}}}$

Here, the question says that volume of the sphere is 850 m³. Radius of sphere is not given to us! , but we need radius to find it's surface area , as surface area of sphere is 4πr². Don't worry! here we have volume (850 m³). So, firstly we will find radius by putting values in formula of volume (vol) of sphere (4/3πr³). After finding radius , we will put it's value in formula of surface area (SA) of sphere. Then we will get our answer.

$\:\:\:\:\:\:\:\:\:\:\large\underbrace{\underline{\sf{So, \:let's\:start\:solving!\::}}}$

$\dag\:\underline{\frak{As\:we\:know\:that\::}}$

$\bigstar\:\underline{\underline {\boxed {\boxed {\sf {Volume_{(Sphere)}\:=\:\dfrac{4}{3}\pi r^3}}}}}$

$\dag\:\underline{\frak{Puttig\:all\:values\:in\:the\:formula\::}}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{850\:=\:\dfrac{4}{3}\:\times\:\dfrac{22}{7}\:\times\:r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{850\:\times\:\dfrac{3}{4}\:\times\:\dfrac{7}{22}\:=\: r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{\dfrac{850\:\times\:3\:\times\:7}{4\:\times\:22}\:=\: r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{\dfrac{17850}{88}\:=\: r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{\dfrac{\cancel{17850}}{\cancel{88}}\:=\: r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{202.84\:=\:r^3}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{\sqrt[3]{202.84}\:=\:r}$

$\:\:\:\:\:\:\:\ratio\implies$ $\tt{5.88\:=\:r}$

$\:\:\:\:\:\:\:\ratio\implies$ $\boxed{\boxed{\tt{r\:=\:5.88}}}$

$\underline{\boxed {\sf {\therefore {Radius\:of\:the\:sphere\:=\:\bold{5.88\:m}}}}}\:\bigstar$

$\large\underline{\bold{Now,}}$

$\bigstar\:\underline{\underline{\boxed{\boxed {\sf {Surface\:area_{(Sphere)}\:=\:4\pi r^2}}}}}$

$\dag\:\underline{\frak{Puttig\:all\:values\:in\:the\:formula\::}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{4\:\times\:\dfrac{22}{7}\:\times\:(5.88)^2}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{4\:\times\:22\:\times\:(5.88)^2}{7}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{4\:\times\:22\:\times\:5.88\:\times\:5.88}{7}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{88\:\times\:5.88\:\times\:5.88}{7}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{88\:\times\:34.5744}{7}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{3042.5472}{7}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\tt{\dfrac{\cancel{3042.5472}}{\cancel{7}}}$

$\:\:\:\:\:\:\:\ratio\longmapsto$ $\boxed{\boxed{\tt{434.6496}}}$

$\underline{\boxed {\sf {\therefore {Surface\:area\:of\:the\:sphere\:\approx\:\bold{434\:m^2}}}}}\:\bigstar$

$\:\:\:\:\:\:\:\:\:\:\:\: \:\:\:{\boxed {\underline {\overline {\bold {\mid\bigstar\:More\:to\:know\:\bigstar\mid}}}}}$

$\star\:\sf\underline{Formulas\:related\:to\:surface\:area(SA)\:and\:volume(vol) \::-}$

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

$\rule{200}4$