Question

A solid cylinder of radius 5/2 cm and ht 10/3 cm is melted into a solid sphere Find the radius of the sphere ​

Answer 1

$\red{\huge{\underline{Answer}}}$

$\boxed{ 2.5 \: cm}$

Given:

Radius of Cylinder, r = 5/2 cm

Height of Cylinder,h = 10/3 cm

To find:

Radius of Sphere = R

Solution:

According to the question,

$\boxed{\huge{Volume\: of \:solid\: cylinder = Volume\: of \: sphere}}$

$\pi \: {r}^{2} \: h \: = \frac{4}{3} \pi \: { R}^{3} \\ \\ \cancel{\pi}\times \frac{5}{2} \times \frac{5}{2} \times \frac{10} {\cancel3} = \frac{4} {\cancel3} \: \cancel{\pi} \: {R}^{3} \\ \\ \frac{5}{2} \times 5 \times 5 = 4 \times {R}^{3} \\ \\ 5 \times 5 \times 5 = 8 \times {R}^{3} \\ \\ {R}^{3} = \frac{125}{8} \\ \\ R = \sqrt[3]{ \frac{125}{8} } \\ \\ R = \frac{5}{2}$

Therefore, radius of sphere is 5/2 cm or 2.5 cm.

Answer 2

Question :-

a solid cylinder of radius 5/2 cm and 10/3cm is melted into a solid sphere find the radius of the sphere ?

Solution :-

Given that ;

• a solid cylinder of radius 5/2
• 10/3 melted into a solid sphere

what we have to find here ?

• we have to find here the radius of the sphere

How to find it ?

=> we can find it by using the volume of the solid cylinder .

What is the formula of solid cylinder ?

=> πr^2 h =4/3πr^3

now,

substituting the values ;

=> π×5/2/×5/2×10/3=4/3πr^2

=> 5/2×5×5 =4×12^3

=> 5×5×5=8×12^3

=> r^3=125/8

=>r=3√125/8

=> r=5/2

=>r=2.5cm

so, the radius of the sphere is 2.5 CM .