Question

A rectangular block of metal has dimensions
31.5m, 115.5 m, 36m. This block is melted to
form sphere. Find the radius of sphere.
26.7m
31.5m
71.8m
42.3m​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

${\huge\tt\bf{GIVEN}}\begin{cases}\sf{A\:rectangular\:block}\\\sf{Dimensions =31.5\:m\times 115.5\:m\times 36\:m}\\ \sf{It is melted to form sphere} \end{cases}$

$\huge \tt \bf {TO\:FIND :-}$

• The radius of the sphere formed

$\huge\tt\bf{SOLUTION :-}$

We know the volume of a cuboid is :-

$\leadsto \huge{\boxed {\tt {lbh}}}$

So,

The volume of rectangular box =

$\leadsto \tt {31.5\:m\times 115.5\:m\times 36\:m}$

$\leadsto \huge {\boxed {\tt {130,977\:{m}^{3}}}}$

So, as the cuboid is melted to form a sphere, the volume remains the same.

We know the formula to find the volume of a sphere :-

$\leadsto \huge {\boxed {\tt {\dfrac {4}{3}\pi {r}^{3}}}}$

So, putting in the values :-

$\leadsto \tt {130,977\:{m}^{3}=\dfrac {4}{3}\times \dfrac {22}{7}\times {r}^ {3}}$

$\leadsto \tt {130,977\times \dfrac {3}{4}\times \dfrac {7}{22}={r}^{3}}$

$\leadsto \tt {31,255.875={r}^{3}}$

$\leadsto \tt {r=\sqrt [3] {31,255.875}}$

$\leadsto \tt {r=31.5\:m}$

So, the radius of the sphere is :-

$\leadsto \huge \red{\boxed {\tt {31.5\:m}}}$

$\rule {200}2$

Answer 2

Answer:

Radius of Sphere = 31.5 m

Step-by-step explanation:

We Have :-

Rectangular Block :-

Length = 31.5 m

Breadth = 115.5 m

Height = 36 m

Rectangular Block is melted and converted to Sphere

To Find :-

Radius of Sphere

Formula Used :-

Volume of Cuboid = Length * Breadth * Height

Volume of Sphere = 4 / 3 π r³

Solution :-

Volume of Cuboid = 31.5 * 115.5 * 36

                              = 130977 m³

Volume of Cuboid = Volume of Sphere

130977 = 4 / 3 * 22 / 7 * r³

r³ = ( 130977 * 7 * 3 ) / ( 4 * 22 )

r³ = 2750517 / 88

r³ = 31255.875

r = 31.5 m

Radius of Sphere = 31.5 m