Question

The number of conical bottles of radius 2 cm and height 1.2 cm that can be filled from a cylindrical bottle of radius 6 cm and height 8 cm, full of liquid, is

• A. 60
• B. 130
• C. 180
• D. 18

Hint:

Do not substitute \(\pi = \frac{22}{7}\) early in volume conversion questions.
Leave \(\pi\) as a symbol, as it will cancel out from the numerator and denominator, saving time and avoiding arithmetic errors!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Liquid is transferred from a fully filled cylindrical bottle to multiple identical conical bottles. We need to find how many such conical bottles can be completely filled.

Step 2: Key Formula or Approach:
The volume of liquid is conserved during transfer:
\[ \text{Number of conical bottles } (N) = \frac{\text{Volume of cylindrical bottle}}{\text{Volume of one conical bottle}} \]
- Volume of a cylinder:
\[ V_{\text{cylinder}} = \pi R^2 H \]
- Volume of a cone:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

Step 3: Detailed Explanation:

• Write down dimensions of the cylinder:
Radius, \(R = 6 \text{ cm}\)
Height, \(H = 8 \text{ cm}\)
Volume:
\[ V_{\text{cylinder}} = \pi \times 6^2 \times 8 = 288\pi \text{ cm}^3 \]

• Write down dimensions of the cone:
Radius, \(r = 2 \text{ cm}\)
Height, \(h = 1.2 \text{ cm}\)
Volume:
\[ V_{\text{cone}} = \frac{1}{3} \pi \times 2^2 \times 1.2 \]
\[ V_{\text{cone}} = \frac{1}{3} \pi \times 4 \times 1.2 = 1.6\pi \text{ cm}^3 \]

• Calculate the number of bottles \(N\):
\[ N = \frac{288\pi}{1.6\pi} \]
The term \(\pi\) cancels out:
\[ N = \frac{288}{1.6} = \frac{2880}{16} = 180 \]


Step 4: Final Answer:
The number of conical bottles that can be filled is 180.