Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.1 mensuration.
we have to find find the height of the cylinder given that the
diameters of the internal and external surfaces of a
hollow spherical shell are 6 cm and 10 cm respectively. If it is melted
and recast into a solid cylinder of diameter 14 cm.
Given,
Internal diameter of hollow spherical shell = 6 cm
So, the internal radius of hollow spherical shell = 6/2 = 3 cm = r
External diameter of hollow spherical shell = 10 cm
So, the external diameter of hollow spherical shell = 10/2 = 5 cm = R
Diameter of the cylinder = 14 cm
So, the radius of cylinder = 14/2 = 7 cm
Let the height of cylinder be taken as h cm
Then, according to the question we have
Volume of cylinder = Volume of spherical shell
π × r2 × h = 4/3 π × (R3 – r3)
π × 72 × h = 4/3 π × (53 – 33)
h = 4/3 x 2
h = 8/3 cm
Therefore, the height of the cylinder = 8/3 cm