Question

the dimensions of metallic cuboid are 44cm ×42cm×21 cm it is molten and recast into a sphere find the surface area of the sphere​

Answer 1

SOLUTION :-

Given,

Length of cuboid = 44 cm

Breadth of cuboid = 42 cm

Height of cuboid = 21 cm

According to the question,

Volume of cuboid = Volume of sphere

$\longrightarrow \quad \sf lbh = \dfrac{4}{3}\pi r^3 \\\\\longrightarrow\quad 44\times42\times 21 = \dfrac{4}{3}\times \dfrac{22}{7}\times r^3 \\\\\longrightarrow \quad r^3=44\times 42\times 21 \times \dfrac{3}{4}\times \dfrac{7}{22} \\\\\longrightarrow \quad r^3=21\times 21 \times 21 \\\\\longrightarrow \quad\bf r = 21$

Radius of the sphere = 21 cm

Surface area of the sphere

          $= \sf 4\pi r^2\\\\= 4 \times \dfrac{22}{7}\times 21 \times 21 \\\\= 4 \times 22 \times 3 \times 21 \\\\= \bf 5544 \ cm^2$

Answer 2

$\huge\fcolorbox{red}{red}{AɴSᴡᴇR}$

THE SURFACE AREA OF THE SPHERE IS 5544 cm².

Step-by-step explanation

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

Dimensions = 44 cm × 42 cm × 21 cm

l = 44 cm

b = 42 cm

h = 21 cm

Cuboid was Melted into = Sphere

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

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

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

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

Volume of the cuboid = 38808 cm³.

____________________________

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

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

____________________________

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

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

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

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

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

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

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