Explanation
Curved surface area of a cylinder of radius "$$R$$" and height $$"h$$" is $$ 2\pi Rh$$.
Given, curved surface area $$=44,4$$ $$m^2$$Therefore, CSA of the given cylinder $$ = 2\times \dfrac {22}{7} \times 0.7\times h= 4.4 $$ sq.cm
$$\Rightarrow \dfrac {44}{10}=\dfrac {44}{7}\times \dfrac {7}{10}\times h$$
$$\Rightarrow h = 1 $$ m
Hence, option 'A' is correct.
Given, radius $$r=10.5$$ cm.
We know, the surface area of a sphere of radius $$r$$ $$ = 4\pi { r }^{ 2 } $$
$$= 4 \times \dfrac {22}{7} \times 10.5 \times 10.5 $$
$$= 1386 {cm}^{2} $$.
Therefore, option $$A$$ is correct.
Given, radius $$r=5.6$$ cm.
We know, the surface area of a sphere of radius $$ r= 4\pi { r}^{ 2 } $$
$$= 4 \times \dfrac {22}{7} \times 5.6 \times 5.6 $$
$$= 394.24 {cm}^{2} $$.
$$ => 4 \times \cfrac {22}{7}\times { r }^{ 2 } = 154 {cm}^{2} $$
$$ => { r }^{ 2 } = \cfrac {49}{4} $$$$ =\cfrac {7}{2} cm $$Volume of a sphere $$ = \cfrac { 4 }{ 3 } \pi { r }^{ 3 } $$
$$= \cfrac {4}{3} \times \cfrac {22}{7} \times \cfrac {7}{2} \times \cfrac {7}{2} \times \cfrac {7}{2} = 179 \cfrac {2}{3} {cm}^{3}$$
Surface area of a sphere of radius $$r$$ $$ = 4\pi { r }^{ 2 }$$
$$= 4 \times \dfrac {22}{7} \times 7 \times 7 $$
$$= 616 {cm}^{2} $$.
Radius of the spherical ball $$ = \cfrac {28}{2} = 14 cm $$
The amount of water it displaces is equal to its volume.
Volume of a spherical ball $$ = \cfrac { 4 }{ 3 } \pi {r }^{ 3 }$$
'$$= \cfrac {4}{3} \times \cfrac {22}{7} \times 14 \times 14 \times 14$$
$$ = \cfrac { 34496 }{3} = 11498\cfrac 23 {cm}^{3} $$
Given, surface area of sphere $$=154 cm^2$$
Surface area of a sphere of radius '$$r$$' $$ = 4\pi { r }^{ 2 } = 154 $$
$$ \Rightarrow 4 \times \dfrac {22}{7}\times { r }^{ 2 } = 154 {cm}^{2} $$
$$ \Rightarrow { r }^{ 2 } = \dfrac {49}{4} $$
$$\Rightarrow r = \dfrac {7}{2} = 3.5 cm$$.
Total surface area of a cylinder of Radius "$$R$$" and height "$$h$$" $$ = 2\pi R(R + h)$$Radius of the base of the cylinder $$ = \dfrac {28}{2} = 14 $$ cm
Hence, total surface area of the cylinder $$ =2\times \dfrac { 22 }{ 7 } \times 14(14 + 20) $$
$$= 2992 cm^2 $$
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