Question

a dimension of a metallic cuboid are 44cm× 42xm×21cm . it is melted and recast inti a sphere. find the surface area of sphere. ​

Answer 1

Answer:

5,544 cm²

Step-by-step explanation:

Volume of cuboid will be same as the volume of sphere.

Therefore,

4/3 π r³ = 44×42×21

on further solving this, we get

r³=9261

Thus, r = 21 cm

Now, surface area for sphere = 4πr²

that is, 5,544 cm²

(r=radius of sphere)

Answer 2

$\huge\fcolorbox{red}{red}{AɴSᴡᴇƦ}$

THE SURFACE AREA OF THE SPHERE IS 5544 cm².

Step-by-step explanation

$\huge\underline{\overline{\bold{\textsf{\pink{GIVEN}}}}}$

Dimensions = 44 cm × 42 cm × 21 cm

$\large{\fbox{\fbox{\color{red}{Length (l) = 44 cm}}}}$

$\large{\fbox{\fbox{\color{red}{Breadth (b) = 42 cm}}}}$

$\large{\fbox{\fbox{\color{red}{Height (h) = 21 cm}}}}$

$\bigstar \: \boxed{\sf{\color{lime}{Volume \: of \: cuboid = l \times b \times h}}}★$

$\sf{\longrightarrow} \: 44 \times 42 \times 21$

$\sf{\longrightarrow} \: 1848 \times 21$

$\sf{\longrightarrow} \: 38808 \: {cm}^{3}$

Volume of the cuboid = 38808 cm³.

____________________ _ _____

$\bigstar \: \boxed{\sf{\color{cyan}{Volume \: of \: sphere= \frac{4}{3}\pi{r}^{3}}}}★$

ATQ Volume of the sphere = Volume of the cuboid

$\sf{\implies} \: \dfrac{4}{3} \times \dfrac{22}{7} \times {(r)}^{3} = 38808$

$\sf{\implies} \: \dfrac{88}{21}\times {(r)}^{3} = 38808$

$\sf{\implies} \: 88r^{3} = 38808 \times 21$

$\sf{\implies} \: 88r^{3} = 814968$

$\sf{\implies} \: r^{3} = {\dfrac{814968}{88}}$

$\sf{\implies} \: r^{3} = 9261$

$\sf{\implies} \: r = \sqrt[3]{9261}$

$\sf{\implies} \: r = 21$

Radius of the sphere = 21 cm

____________________________

$\bigstar \: \boxed{\sf{\color{lime}{Surface \: area \: of \: sphere =4\pi{r}^{2}}}}★$

$\sf{\longrightarrow} \: 4 \times \dfrac{22}{7} \times {(21)}^{2}$

$\sf{\longrightarrow} \: 4 \times \dfrac{22}{7} \times 21 \times$

$\sf{\longrightarrow} \: 4 \times 22\times 21 \times 3$

$\sf{\longrightarrow} \:88\times63$

$\sf{\longrightarrow} \: 5544 \: {cm}^{2}$

Therefore, the surface area of the sphere is 5544 cm².