Question -
Answer -
Given,
Internal diameter ofthe hollow sphere = 6 cm
So, the internalradius of the hollow sphere = 6/2 cm = 3 cm = r
External diameter ofthe hollow sphere = 10 cm
So, the externalradius of the hollow sphere = 10/2 cm = 5 cm = R
We know that,
Volume of the hollowspherical shell = 4/3 ╧А ├Ч (R3┬атАУ r3)
= 4/3 ╧А ├Ч (53┬атАУ33)┬а┬а┬а┬а┬а┬а┬а┬а тАж..┬а (i)
And given, the lengthof the solid cylinder = 8/3 cm
Let the radius of thesolid cylinder be r cm
We know that,
Volume of the cylinder= ╧А ├Ч r2┬а├Ч h
= ╧А ├Ч r2┬а├Ч8/3┬а ┬а┬а┬а┬а┬атАж.. (ii)
Now equating both (i)and (ii), we have
4/3 ╧А ├Ч 53┬атАУ33┬а= ╧А ├Ч r2┬а├Ч 8/3
4/3 x (125 тАУ 27) = r2┬а├Ч8/3
98/2 = r2
r2┬а=49
r = 7
So, d = 7 x 2 = 14 cm
Therefore, thediameter of the cylinder is 14 cm