Question

Find the Surface Area of the sphere having radius :-

i) 10.5 cm
ii) 5.6 cm
iii) 14 cm

​​

Answer 1

Answer:

Question :

Find the Surface Area of the sphere having radius :-

• i) 10.5 cm
• ii) 5.6 cm
• iii) 14 cm

Solution :

As we know that :

${\pink{\underline{\boxed{\bf{Surface \: Area_{(Sphere)} = 4\pi{r}^{2}}}}}}$

Where :

• π = 22/7
• r = radius

━━━━━━━━━━━━━━━━━━━━

i) 10.5 cm

Here's the diagram of sphere with radius 10.5 cm. See this diagram from website Brainly.in.

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf{10.5\ cm}}\end{picture}$

Finding the surface area of sphere :

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

${\implies{\sf{Surface \: area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(10.5)}^{2}}}}$

${\implies{\sf{Surface \: area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(10.5\times 10.5)}}}}$

${\implies{\sf{Surface \: area_{(Sphere)} = 4 \times \dfrac{22}{7} \times 110.25}}}$

${\implies{\sf{Surface \: area_{(Sphere)} = 4 \times \dfrac{22}{\cancel{7}} \times \cancel{110.25}}}}$

${\implies{\sf{Surface \: area_{(Sphere)} = 4 \times 22 \times 15.75}}}$

${\implies{\sf{\red{Surface \: area_{(Sphere)} = 1386\: {cm}^{2}}}}}$

Hence, the surface area of sphere is 1386 cm².

$\rule{190}1$

ii) 5.6 cm

Here's the diagram of sphere with radius 5.6 cm. See this diagram from website Brainly.in.

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf{5.6\ cm}}\end{picture}$

Finding the surface area of sphere :

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

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(5.6)}^{2}}}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(5.6 \times 5.6)}}}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times 31.36}}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{\cancel{7}} \times \cancel{31.36}}}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times 22 \times 4.48}}}$

${\implies{\sf{\red{Surface \:area_{(Sphere)} = 394.24 \: {cm}^{2}}}}}$

Hence, the surface area of sphere is 394.24 cm².

$\rule{190}1$

iii) 14 cm

Here's the diagram of sphere with radius 14 cm. See this diagram from website Brainly.in.

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf{14\ cm}}\end{picture}$

Finding the surface area of sphere :

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

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(14)}^{2} }}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times {(14 \times 14)} }}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{7} \times 196 }}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times \dfrac{22}{\cancel{7}} \times \cancel{196}}}}$

${\implies{\sf{Surface \:area_{(Sphere)} = 4 \times 22 \times 28}}}$

${\implies{\sf{\red{Surface\:area_{(Sphere)} = 2464 \: {cm}^{2}}}}}$

Hence, the surface area of sphere is 2464 cm².

$\rule{220pt}{4pt}$

Answer 2

Step-by-step explanation:

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

(i) r=10.5cm

SA=4πr2=4×722×1010.5×1010.5

=10088×15×105

${ \longmapsto{ \sf{ \boxed{ \green{ \pmb{ \sf=1386 cm^2 }}}}}}$

Hence, the surface area of sphere is 1386cm².

(ii) r=5.6cm

SA=4πr2

${ \longmapsto{ \sf{=[4×722×(5.6)2]cm {}^{2} }}}$

${ \longmapsto{ \sf{ =[788×105.6×105.6]cm{}^{2} }}}$

${ \longmapsto{ \sf{ \boxed{ \green{ \pmb{ \sf=394.24 cm2 }}}}}}$

Hence, the surface area of sphere is 394.24 cm².

(iii) r=14cm, 

SA=4πr2

${\longmapsto{ \sf{=4×722×14×14}}}$

$\longmapsto{ \sf{ \boxed{ \green{ \pmb{ \sf{=2464 cm {}^{2} }}}}}}$

Hence, the surface area of

 sphere is 2464 cm².

 тнαηк үσυ !!!❄

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