Question

the ratio of rdii of two cylinders is 1 : 2. If the ratio of their heights is 2 : 1, then the ratio of their
volumes will be?​

Answer 1

QUESTION:-

the ratio of rdii of two cylinders is 1 : 2. If the ratio of their heights is 2 : 1, then the ratio of their volumes will be?

SOLUTION:-

➠let, the h1 , h2 be the height of two cylinder and r1 , r2 be their radii.

➠ Given, the ratio of height is 2:1.

➠ .°. h1 / h2 = 2/1

➠ also, given the ratio of radii 1:2

➠ .°. r1 / r2= 1/2

➠ volume of first cylinder,

➠ (V1)=π(r1)²h1

➠ volume of second cylinder,

➠ (V2)=π(r2)²h2

NOW,

➠ V1:V2= π(r1)²h1 : π(r2)²h2

➠V1:V2=(r1)²h1 : (r2)²h2

➠ .°. V1/V2=((r1)²/r2)² ) ((h1/h2)

➠ .°. V1/V2 = (1/2)² (2/1)

➠ .°. V1/V2= 1/4 × 2/1

➠ .°. V1/V2=1/2

➠ .°. V1:V2 = 1:2

.°. the ratio of two cylinder is 1:2.

Answer 2

Answer:

• Ratio of their volumes = 1:2.

Given :

• The ratio of rdii of two cylinders is 1 : 2.

• The ratio of their heights is 2 : 1

To find :

• The ratio of their volumes will be = ?

Step-by-step explanation:

Let r and r₁ be the radii of the given cylinders and V and V₁ be their volumes.

Since the ratio of their radii is 1:2,therefore their radii are 1x and 2x.

Again let h and h₁ be the height of the given cylinders and their ratio is 2:1.

∴ Their heights are 2x and 1x.

∴ V = Π(1x)²(2y) [∴ volume of cylinders =πr²h]

and V₁ =π(2x)²(1y)

∴ V/V₁ = π*1x*1x*2y/π*2x*2x*1y=1*1*2/2*2*1=2/4=1/2

Thus, ratio of their volumes is 1:2