Let A and B be two cylinders such that the capacity of A is the same a

1.	Let A and B be two cylinders such that the capacity of A is the same as the capacity of B. The ratio of the diameters of A and B is 1 ∶ 4. What is the ratio of the heights of A and B?1. 16 : 32. 16 : 13. 1 : 164. 3 : 16
Answer» Correct Answer - Option 2 : 16 : 1 Given: The capacity of cylinders A and B are equal. Volume₍_A) = Volume₍_B) The ratio of diameters = A ∶ B = 1 ∶ 4 Formula Used: Volume of cylinder = πr²h Diameter = 2 × r Where, r → Radius of the cylinder h → Height of the cylinder Calculation: r = D/2 The ratio of the radius of A and B \(\Rightarrow \frac{{Diamater\;of\;A}}{{Diameter\;of\;B}} = 1/4\) The capacity of cylinders A and B are equal. Volume(A) = Volume(B) ⇒ π× r_(A)²× h_(A) = π× r_(B)²× h_(B) ⇒ r(A)2× h(A) = r(B)2× h(B) ⇒ r(A)2/r(B)2 = h(B)/ h(A) ⇒1²/4² = h(B)/ h(A) ⇒1/16 = h(B)/ h(A) ⇒ h_(A)/h_(B) = 16/1 ⇒ h(A) : h(B) = 16 : 1 ∴ The ratio of the heights of A and B is 16 ∶ 1.

Let A and B be two cylinders such that the capacity of A is the same as the capacity of B. The ratio of the diameters of A and B is 1 ∶ 4. What is the ratio of the heights of A and B?1. 16 : 32. 16 : 13. 1 : 164. 3 : 16

Answer» Correct Answer - Option 2 : 16 : 1

Given:

The capacity of cylinders A and B are equal.

Volume₍_A) = Volume₍_B)

The ratio of diameters = A ∶ B = 1 ∶ 4

Formula Used:

Volume of cylinder = πr²h

Diameter = 2 × r

Where,

r → Radius of the cylinder

h → Height of the cylinder

Calculation:

r = D/2

The ratio of the radius of A and B

\(\Rightarrow \frac{{Diamater\;of\;A}}{{Diameter\;of\;B}} = 1/4\)

The capacity of cylinders A and B are equal.

Volume(A) = Volume(B)

⇒ π× r_(A)²× h_(A) = π× r_(B)²× h_(B)

⇒ r(A)2× h(A) = r(B)2× h(B)

⇒ r(A)2/r(B)2 = h(B)/ h(A)

⇒1²/4² = h(B)/ h(A)

⇒1/16 = h(B)/ h(A)

⇒ h_(A)/h_(B) = 16/1

⇒ h(A) : h(B) = 16 : 1

∴ The ratio of the heights of A and B is 16 ∶ 1.