Question

10 identical metallic cylinders of radius 3 cm are melted to form one cylinder of radius 15 cm. Find the ratio of their heights.​

Answer 1

Answer:

5:2

Step-by-step explanation:

The radius of the metallic cylinder, r is 3 cm.

Therefore the volume of the metallic cylinder, v = πr^2h = 9hπ cm^3.

As 10 identical cylinders are melted to form a big cylinder, the volume V of the big metallic cylinder is 10 times the volume v of the smaller cylinder.

Therefore, The volume of big metallic cylinder, V = 10 * v = 10 * 9hπ = 90hπ $cm^3$.

The radius of the big metallic cylinder, R is 15 cm.

Let H denote the height of the big cylinder.

Therefore, The volume of the big metallic cylinder, V= πR^2H = π(15^2)H = 225Hπ cm^3.

thus we get, $90h\pi = 225H\pi$ ⇒ $h/H = 225\pi /90\pi =5/2$