Question

iii) if the surface area of a sphere is 2826 cm2 then find its volume. (i = 3.14)
Sol​

Answer 1

Appropriate Question :

• If the surface area of a sphere is 2826cm² then find its volume. (π = 3.14).

Solution :

Given that,

• Surface area of a sphere is 2826cm².

And we need to find out the volume of sphere.

We know that,

• Surface area of sphere = 4πr².
• Volume of sphere = 4/3πr³.

So,

→ Surface area of sphere = 4πr²

→ 2826 = 4 * 3.14 * r²

→ 2826 = 12.56 * r²

→ 2826 = 12.56r²

→ r² = 2826/12.56

→ r² = 225

→ r = √225

→ r = 15.

Now,

→ Volume of sphere = 4/3πr³

→ Volume of sphere = 4/3 * 3.14 * (15)³

→ Volume of sphere = 4/3 * 3.14 * 3375

→ Volume of sphere = 4/3 * 10597.5

→ Volume of sphere = 4 * 3532.5

→ Volume of sphere = 14130. (Ans.)

Hence, the volume of sphere is 14130cm³.

Learn more :

1. if area of hemisphere is 28,000m2 find the diameter of hemisphere

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2. ind the volume and surface area of the following cuboid. length=8cm ,breadth=7.5cm,height=12cm

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Answer 2

${ \underline{ \underline{ \huge{ \red{ \tt{QUESTION}}}}}}$

If the surface area of a sphere is 2826 cm^2 . Then find its volume. ( π = 3.14 )

${ \underline{ \underline{ \huge{ \red{ \tt{SOLUTION}}}}}}$

${ \dag{ \underline{ \underline{ \green{ \tt{ \: \: given}}}}}} \\ \\ { \sf{ \blue{surface \: area \: of \: sphere = 2826 \: {cm}^{2} }}}$

${ \dag{ \underline { \underline{ \tt{ \green{ \: \: \: to \: find}}}}}} \\ \\ { \sf{volume \: of \: the \: sphere}}$

${ \boxed{ \boxed{ \green{ \sf{surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}}$

${ : { \implies{ \sf{ \blue{2826 \: {cm}^{2} = 4\pi {r}^{2} }}}}} \\ \\ \\ { : { \implies{ \sf { \blue{ {r}^{2} = \frac{2826 {cm}^{2} }{4 \times \pi}}}}}} \\ \\ \\ { : { \implies{ \sf { \blue{r = \sqrt{ \frac{2826 \: {cm}^{2} }{4 \times \pi} } }}}}}$

${ \boxed{ \boxed{ \sf{ \green{volume \: of \: sphere = \frac{4}{3} \pi {r}^{3}}}}}}$

${ : { \implies{ \sf{ \red{volume = \frac{4}{3} \pi {( \sqrt{ \frac{2826}{4 \times \pi} }) }^{3} }}}}} \\ \\ \\ { : { \implies{ \sf{ \red{volume = \frac{4}{3} \pi ({ \frac{53.16}{2 \times 1.77} }^{3}) }}}}} \\ \\ \\ { : { \implies{ \sf{ \red{volume = \frac{4}{3} \times 3.14 \times \frac{53.16 \times 53.16 \times 53.16}{8 \times 1.77 \times 1.77 \times 1.77}}}}}}$

${ : { \implies{ \sf { \red{volume = \frac{4}{3} \times 3.14 \times \frac{150229}{44.36}}}}} } \\ \\ \\ { : { \implies{ \sf{ \red{volume = \frac{4}{3} \times 3.14 \times 3386 \: {cm}^{3} }}}}}$

${ : { \implies{ \red{ \sf{volume = \frac{42528}{3} {cm}^{3} }}}}} \\ \\ \\ { : { \implies{ \red{ \sf{ volume = 14176 \: {cm}^{3}}}}}}$