Question

Two cylindrical cans have bases of same size. The diameter of each is the 14cm. One of the cans is 10cm high and other is 20cm high. Find the ratio of their volumes.

Answer 1

→ Given ←

• Two cylindrical cans have bases of same size.
• The diameter of each is the 14 cm.
• One of the cans is 10 cm high and other is 20 cm high.

• Radius of the both the cans (r₁, r₂) = 7 cm
• Height of the first can (h₁) = 10 cm
• Height of the second can (h₂) = 20 cm

$\rule{180}2$

→ To Find ←

The ratio of their volumes.

$\rule{180}2$

→ We Must Know ←

Volume of a cylinder = $\sf{\pi r^2 h}$

Where,

• r is the radius
• h is the height.

$\rule{180}2$

→ Solution ←

◙ Volume of the first can(V₁) = $\sf{\pi(r_1)^2 h_1}$ =  $\sf{\pi (7)^2 \times 10}$

◙ Volume of the first can(V₂) = $\sf{\pi(r_2)^2 h_2}$ = $\sf{\pi (7)^2 \times 20}$

Ratio of their volumes :-

$\displaystyle{\sf{\dashrightarrow \frac{V_1}{V_2}=\frac{\pi (7)^2 10}{\pi (7)^2 20} }}\\\\\displaystyle{\sf{\dashrightarrow \frac{V_1}{V_2}=\frac{10}{20} }}\\\\\displaystyle{\sf{\dashrightarrow \frac{V_1}{V_2}= \frac{1}{2} }}$

Hence, the ratio of their volumes is 1 : 2.

Answer 2

Given :

• Two cylindrical cans have bases of same size.

• The diameter of each is the 14cm.

• One of the cans is 10cm high and other is 20cm high.

To find :

• The ratio of their volumes =?

Step-by-step explanation :

The diameter of each is the 14cm.

Radius = Diameter /2

Substituting the values, we get,

= 14/2

= 7.

Therefore, Radius of both cans = 7 cm

Height (h) of the first can = 10 cm. [Given]

Height(H) of the second can = 20 cm [Given]

We know that,

Volume of cylinder = πr²h

Now,

Volume of first Cylinder = πr²h

Volume of second Cylinder = πr²H

According to the question :

Volume of first Cylinder / Volume of second Cylinder

Or,

πr²h / πr²H

Substituting the values in the above formula we get,

= πr²h / πr²H

= h/H

= 10/20

= 1/2

Therefore, the ratio of their volumes = 1 : 2