Question

The volume of sphere is 4852cm³.Then its surface area is

Answer 1

Answer:

Given :-

• The volume of sphere is 4852 cm³.

To Find :-

• What is the surface area of the sphere.

Formula Used :-

$\clubsuit$ Volume of Sphere Formula :

$\mapsto \sf\boxed{\bold{\pink{Volume_{(Sphere)} =\: \dfrac{4}{3}{\pi}r^3}}}$

$\clubsuit$ Surface Area Of Sphere Formula :

$\mapsto \sf\boxed{\bold{\pink{Surface\: Area_{(Sphere)} =\: 4{\pi}r^2}}}$

where,

• π = pie or 22/7
• r = Radius

Solution :-

First, we have to find the value of radius of the sphere :

Given :

• Volume of Sphere = 4852 cm³

According to the question by using the formula we get,

$\implies \sf \dfrac{4}{3} \times \dfrac{22}{7} \times r^3 =\: 4852$

$\implies \sf \dfrac{88}{21} \times r^3 =\: 4852$

$\implies \sf r^3 =\: \dfrac{4852 \times 21}{88}$

$\implies \sf r^3 =\: \dfrac{101892}{88}$

$\implies \sf r^3 =\: 1157.86$

$\implies \sf r =\: \sqrt[3]{1157.86}$

$\implies \sf\bold{\purple{r =\: 10.50\: cm}}$

Now, we have to find the surface area :

Given :

• Radius (r) = 10.50 cm

According to the question by using the formula we get,

$\longrightarrow \sf Surface\: Area_{(Sphere)} =\: 4 \times \dfrac{22}{7} \times (10.50)^2$

$\longrightarrow \sf Surface\: Area_{(Sphere)} =\: \dfrac{88}{7} \times 10.50 \times 10.50$

$\longrightarrow \sf Surface\: Area_{(Sphere)} =\: \dfrac{88}{7} \times 110.25$

$\longrightarrow \sf Surface\: Area_{(Sphere)} =\: \dfrac{\cancel{9702}}{\cancel{7}}$

$\longrightarrow \sf \bold{\red{Surface\: Area_{(Sphere)} =\: 1386\: cm^3}}$

$\therefore$ The surface area of sphere is 1386 cm³.

Answer 2

Solution -

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Suppose that the sphere has a radius of r.

The volume of the sphere is 4852 cm³ .

> 4/3 π r³ = 4852

> πr³ = 3639

> 3.14 r³ = 3639

> r³ = 1158.974 ..

> r = (1158.9754)^⅓

> r ≈ 10.5 cm

Surface area of the sphere :

> 4 π r²

> 4 × 3.14 × 10.5 × 10.5

> 1385 cm² approximately .

Answer - The surface area of the sphere Is 1385 cm² approximately.

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Additional Information -

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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