Question

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

Answer 1

Step by step solution :

Given :

diameter of solid cylinder is = 2 cm

Radius of solid cylinder, r=1 cm

What to find out = length of solid cylinder?

Formula used: πr^2h

Solution :

Volume of solid cylinder =πr^2h

=π×[1]^2×h=πh ===> [ equation (1)]

Length of hallow cylinder, H=16 cm

External diameter =20 cm

External radius =10 cm

Thickness = 2.5 mm= 0.25 cm

Internal radius = external radius - thickness =(10-0.25) cm= 9.75 cm

Volume of hallow cylinder, V=$pie (22/7) (r_1 {}^{2} - r_2 {}^{2} )×h$

$π(10 {}^{2} - (9.75) {}^{2} ) \times 16 </p><p></p><p></p><p></p><p><strong>=16π \times 19.75 \times 0.25$ =>[equation (2)]

From equation [1] and [2] We get:

$πh = 16π \times 19.75 \times 0.25$

Hence, h=

$16 \times 19.75 \times 0.25 = 79 \: cm$

Therefore the length of solid cylinder is =79 cm

Extra :✈

• Solid cylinder =A cylinder is a three-dimensional shape in geometry. A cylinder is round and has a top and bottom in the shape of a circle. The top and bottom are flat and always the same size. I think the best way to describe the shape of a cylinder is to think of a can of soup.

• Hollow cylinder =A hollow cylinder is a cylinder which is vacant from inside and has some difference between the internal and external radius.