Question

Find the surface area of sphere of radius 8 cm.

​

Answer 1

Radius of sphere = 8 cm

Now , we have to find out surface area of sphere.

We know that , surface area of sphere ( A)= 4π r²

$\rm \rightarrow A = 4 \pi {r}^{2} \\ \\ \rm \rightarrow A = 4 \times 3.14 \times {(8)}^{2} \\ \\\rm \rightarrow A = 4 \times 3.14 \times 64 \\ \\\rm \rightarrow A = 803.84 \: {m}^{2}$

surface area of sphere ( A) = 803.84 m²

Additional Information :

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = (4/3)πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

Answer 2

${\large{\bold{\sf{\bf{\underbrace{Understanding \; the \; question}}}}}}$

➥ This question says that we have to find the surface area of sphere whose radius is 8 cm.

${\large{\bold{\sf{\underline{Given \; that}}}}}$

➥ Radius of sphere = 8 cm

${\large{\bold{\sf{\underline{To \; find}}}}}$

➥ Surface area of sphere.

${\large{\bold{\sf{\underline{Solution}}}}}$

➥ Surface area of sphere = 803.84 m²

${\large{\bold{\sf{\underline{Using \: concept}}}}}$

➥ Surface area of sphere formula

${\large{\bold{\sf{\underline{Using \: formula}}}}}$

➥ Surface area of sphere = 4πr²

${\large{\bold{\sf{\underline{Where,}}}}}$

➥ π is pronounced as pi

➥ Value of π is ${\bold{\sf{\dfrac{22}{7}}}}$ or 3.14

➥ r denotes Radius

➥ ² means square

${\large{\bold{\sf{\underline{Full \; Solution}}}}}$

~ Finding Surface Area of sphere

${\bullet}$ Surface Area = 4πr²

${\bullet}$ Surface Area = 4 × ${\bold{\rm{\dfrac{22}{7}}}}$ × 8²

${\bullet}$ Surface Area = 4 × ${\bold{\rm{\dfrac{22}{7}}}}$ × 64

${\bullet}$ Surface Area = ${\bold{\rm{\dfrac{88}{7}}}}$ × 64

${\bullet}$ Surface Area = ${\bold{\rm{\dfrac{5632}{7}}}}$

${\bullet}$ Surface Area = 803.84 m²

${\frak{\green{Henceforth, \: 803.84^{2} \: m \: is \: the \: surface \: area \: of \: sphere}}}$

${\Large{\bold{\sf{\bf{\underbrace{Additional \; knowledge}}}}}}$

Sphere diagram -

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf R}\end{picture}$

Some formulas related to circle -

${\large{\pink{\bold{\sf{Area \; of \; circle = \pi r^{2}}}}}}$

${\large{\pink{\bold{\sf{Circumference \; of \; circle = 2 \times \pi \times r}}}}}$

${\large{\pink{\bold{\sf{Diameter \; of \; circle = 2 \times r}}}}}$

${\large{\pink{\bold{\sf{Radius \; of \; circle = \dfrac{Diameter}{2}}}}}}$