Question

The height of a cylinder is 2/3 of its diameter. If the volume of that cylinder is equal to the sphere of radius 4 cm, find the radius of the cylinder's base.​

Answer 1

Given that,

➜ Height of a cylinder is 2/3 of its diameter.

➜ Volume of the cylinder is equal to the volume of a sphere of radius 4 cm.

We need to find,

➜ Radius of the cylinder's base

Now,

⇒ Volume of Sphere = (4πr³) / 3

⇒ V = (4 × 4³ × π) / 3

⇒ V = 256π / 3 cm³ ...(1)

Again,

Let the radius of cylinder be r, then

⇒ Height of cylinder = 4r/3

Also,

⇒ Volume of cylinder = Volume of the sphere

⇒ π(radius)²(height) = 256π / 3 [ from (1) ]

⇒ π(r)²(4r / 3) = 256π / 3

⇒ 4πr³ = 256π

⇒ r³ = 256/4

⇒ r³ = 64

∴ Radius, r = 4 cm

Some Information :-

◉ Volume of Hemisphere = 2πr³ / 3

◉ Volume of Cube = (Side)³

◉ Volume of Cone = (πr²h) / 3

◉ Volume of Cuboid = Length × Breadth × Height

Where, r = radius