Question

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the surface area of a sphere is 452 4/7cm^2.what is its volume?

Answer 1

Given that :-

Surface area of sphere = 452 (4/7) cm²

We know that surface area of a sphere = 4πr²

=>
$4\pi r {}^{2} = 452 \frac{4}{7}$

Taking π as 22/7, we get

$4 \times \frac{22}{7} \times {r}^{2} = 452 \frac{4}{7} \\ \\ = > \frac{88}{7} \times {r}^{2} = \frac{3168}{7}$

since 452 (4/7) = 3168/7

(In its improper fraction form)

=>
${r}^{2} = \frac{3168}{7} \times \frac{7}{88} \\ \\ = > {r}^{2} = 36 \\ \\ = > r = \sqrt{36} \\ \\ = > r = 6$

So we get that the radius is 6 cm

So volume of sphere = 4/3 × πr³

=>
$\frac{4}{3} \times \frac{22}{7} \times {6}^{3} \\ \\ = > \frac{4}{3} \times \frac{22}{7} \times 216 \\ \\ = 4 \times \frac{22}{7} \times 72 \\ \\ = \frac{6336}{7}$


Answer :- The volume of sphere is 6336/7 cm³

or

905.14 cm³ (approx)

Answer 2

Answer :

905. 14 cm³

Step-by-step explanation :

Total surface area of sphere = 4 π r²

⇒ 4 π r² = 452 $\sf \frac{4}{7}$

⇒ 4 π r² = $\sf \frac{3168}{7}$

⇒ π r² =  $\sf \frac{3168}{7} \times 4$

⇒ r² =  $\sf \frac{3168}{7} \times \frac{7}{22} \times 4$

⇒ r² = 36

⇒ r = √36

⇒ r = 6 cm

Now,

Volume of sphere =  $\sf \frac{4}{3}$ π r³

⇒ 4 / 3 × 22 / 7 × 6³

⇒ 4 × 22 × 36 × 2 / 7

⇒ 6337 / 7

Hence, the volume of sphere is 905.14 cm³