This question is from r d sharma class 10 maths.
I found this question while doing maths class 10. I need help in getting the solution.
In this question we have to find the diameter of the cylinder given that the diameters of internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 8/3.
Given,
Internal diameter of the hollow sphere = 6 cm
So, the internal radius of the hollow sphere = 6/2 cm = 3 cm = r
External diameter of the hollow sphere = 10 cm
So, the external radius of the hollow sphere = 10/2 cm = 5 cm = R
We know that,
Volume of the hollow spherical shell = 4/3 π × (R3 – r3)
= 4/3 π × (53 – 33) ….. (i)
And given, the length of the solid cylinder = 8/3 cm
Let the radius of the solid cylinder be r cm
We know that,
Volume of the cylinder = π × r2 × h
= π × r2 × 8/3 ….. (ii)
Now equating both (i) and (ii), we have
4/3 π × 53 – 33 = π × r2 × 8/3
4/3 x (125 – 27) = r2 × 8/3
98/2 = r2
r2 = 49
r = 7
So, d = 7 x 2 = 14 cm
Therefore, the diameter of the cylinder is 14 cm