Question

TEL
If the radius of the base of a right circular cylinder is halved, keeping the height
Same, find the ratio of the volume of the reduced cylinder to that of the original
cylinder​

Answer 1

$\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}$

Let the radius of the cylinder is r and height is h

• ∴ Volume of the cylinder = πr 2 h

According to the question new radius is half of the initial radius

• ∴New radius= 2r

Height is h.

• ∴New volume of the cylinder = π( 2r )2

h=π 4r 2 h

∴ The ratio of the new volume of the cylinder and initial volume of the original cylinder=

• πr 2 hπ 4r 2 h = 41

∴ Ratio =1:4.

Answer 2

Let the radius of the cylinder is r and height is h

• ∴ Volume of the cylinder = πr 2 h

According to the question new radius is half of the initial radius

• ∴New radius= 2r

Height is h.

• ∴New volume of the cylinder = π( 2r )2

h=π 4r 2 h

• ∴ The ratio of the new volume of the cylinder and initial volume of the original cylinder=

πr 2 hπ 4r 2 h = 41

• ∴ Ratio =1:4.

Mark ❤️