Question

It is given that ..the volume of a sphere is 38808cm^{3} find it's radius as well as C.S.A ( curved surface area.)​

Answer 1

Given :

• The volume of a sphere is 38808 cm³.

To find :

• It's radius as well as C.S.A ( curved surface area.) =?

Step-by-step explanation :

As We know that,

Volume of a sphere = 4/3 πr³

Substituting the values in the above formula, we get,

➮ 38808 = 4/3 × π × r³

➮ 4πr³ = 38808 × 3

➮ 4πr³ = 116,424

➮ πr³ = 116,424/4

➮ πr³ = 29,106

➮ r³ = 29,106 ÷ (22/7)

➮ r³ = 29,106 × 7/22

➮ r³ = 203,742/22

➮ r³ = 9261

➮ r = 21

Therefore, Radius of sphere = 21 cm.

Now,

As per question,

Curved Surface Area of sphere = 4πr²

Substituting the values in the above formula, we get,

= 4 × π × 21 × 21

= 1,764π

Therefore, Curved Surface Area of sphere = 1764π.

Answer 2

AnSwer:-

• Radius of the sphere = 21cm
• Curved Surface Area of the sphere = 5544cm²

Given:-

• Volume of the Sphere = 38808cm³

To Find :-

• Curved Surface Area and Radius of the Sphere.

Explanation :-

${ \bigstar{ \underline{According \: to \: the \: question,}}}$

${\sf {\: Volume \: of \: Sphere = \: \dfrac{4}{3}\pi \: {r}^{3} }} \\ \\ : \implies \: 38808 = \dfrac{4}{3} \times \frac{22}{7} \times {r}^{3} \\ \\ : \implies \: 38808= \frac{4 \times 22 \times {r}^{3} }{3 \times 7} \\ \\ : \implies \:38808 = \frac{88 \times {r}^{3} }{21} \\ \\ : \implies \: \frac{ \cancel{38808} \times 21}{ \cancel{88}} = {r}^{3} \\ \\ : \implies \:441 \times 21 = {r}^{3} \\ \\ : \implies \:21 \times 21 \times 21 = {r}^{3} \\ \\ : \implies \: { \sf{ \boxed{ \blue{r = 21cm}}}}$

Now,

$\sf \: Curved \: Surface \: Area = 4\pi \:{r}^{2} \\ \\ \ : \implies \:4 \times \frac{22}{7} \times {21}^{2} \\ \\ : \implies \: \frac{4 \times 22 \times 21 \times \cancel{21}}{ \cancel 7} \\ \\ : \implies \:4 \times 22 \times 21 \times 3 \\ \\ : \implies \:88 \times 63 \\ \\ : \implies { \boxed{ \blue{\:5544 {cm}^{2}}}}$

Therefore, radius and CSA of sphere are 21cm and 5,544cm² respectively.