Question

a solid cylinder of radius 10 cm and length 1000 cm, a cylindrical hole is made into it to obtain a cylindrical shell of uniform thickness and having a volume equal to one-fourth of the original cylinder. the thickness of the cylindrical shell is ____ and with solution

Answer 1

Step-by-step explanation:

Radius of the cylinder= 10 cm,

Height of the cylinder= 1000 cm.

So, volume of that cylinder= π R²h,

= π (10)²× 1000.

= 100000π cm.

Now, the volume of the smaller cylinder= 1/4 of original cylinder= 100000×π/4,

= 25000 cm³.

But wait, I can also conclude that the volume of the smaller one = π × r² h,

So, what if I compare these quantities???

• π r²h= 25000 cm³,
• then finding the value of r,

$\frac{25000 \times \pi}{\pi \times 1000} \\ = 25 \: cm$

So, the radius of the cylinder = 25 cm.