Question

Two similar cylindrical tins have base radii 4cm and 7cm. If the capacity of smaller tin is 230 cm3, find the capacity of larger tin​

Answer 1

Given:

• Radius of similar cylinderical tin = 4cm and 7cm
• Capacity of smaller tin = 230cm³

Find:

• Capacity of larger tin.

Solution:

Let, the radius of larger tin "R" cm

and radius of smaller tin "r" cm

Height of both cylinder are same "h" cm

Now, we know that

↣ Volume of Cylinder = πr²h

So,

¤ (Volume of smaller Cylinder)/(Volume of larger cylinder) = πr²h/πR²h

¤ V₁/V₂ = πr²h/πR²h

where,

• V₁ = 230cm³
• r = 4cm
• R = 7cm

♛ Substituting these values ♛

↦V₁/V₂ = πr²h/πR²h

↦230/V₂ = π(4)²h/π(7)²h

↦230/V₂ = (4)²/(7)²

↦230/V₂ = 16/49

• Cross - multiplication •

↦ 16V₂ = 230 × 49

↦ 16V₂ = 11270

↦ V₂ = 11270/16

↦ V₂ = 704.375cm³

Hence, capacity of larger cylindrical tin will be 704.375cm³