Question

Find the surface area of a sphere of diameter:
(i) 14 cm
(ii) 21 cm
(iii) 35cm​

Answer 1

Given :

• Diameters are 14 cm , 21 cm , 25 cm .

To Find :

• Surface Area of Sphere .

Solution :

(i) 14 cm

$\longmapsto\tt{Radius=\cancel\dfrac{14}{2}=7\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Surface\:Area\:of\:Sphere=4\pi{{r}^{2}}}$

Putting Values :

$\longmapsto\tt{4\times\dfrac{22}{{\not{7}}}\times{{\not{7}}}\times{7}}$

$\longmapsto\tt{4\times{22}\times{7}}$

$\longmapsto\tt\bf{616\:{cm}^{2}}$

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(i) 21 cm

$\longmapsto\tt{Radius=\cancel\dfrac{21}{2}=10.5\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Surface\:Area\:of\:Sphere=4\pi{{r}^{2}}}$

Putting Values :

$\longmapsto\tt{4\times\dfrac{22}{{\cancel{7}}}\times\dfrac{{\cancel{105}}}{10}\times\dfrac{105}{10}}$

$\longmapsto\tt{\dfrac{138600}{100}}$

$\longmapsto\tt\bf{1386\:{cm}^{2}}$

_______________________

(i) 35 cm

$\longmapsto\tt{Radius=\dfrac{35}{2}}$

Using Formula :

$\longmapsto\tt\boxed{Surface\:Area\:of\:Sphere=4\pi{{r}^{2}}}$

Putting Values :

$\longmapsto\tt{{\cancel{4}}\times\dfrac{22}{{\cancel{7}}}\times\dfrac{{\cancel{35}}}{{\cancel{2}}}\times\dfrac{35}{{\cancel{2}}}}$

$\longmapsto\tt{22\times{5}\times{35}}$

$\longmapsto\tt\bf{3850\:{cm}^{2}}$