Question

Ice-cream,completely filled in a cylinder of diameter 35 cm and height 32 cm,is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm.The maximum number of cones that can be used in this way is

• A. 950
• B. 1000
• C. 1050
• D. 1100

Answer 1

The Correct Option is C

The volume of the ice cream in the cylinder is:

$$V_{\text{cylinder}} = \pi r^2 h = \pi \left( \frac{35}{2} \right)^2 \times 32 = \pi \times 17.5^2 \times 32 \approx 3.1416 \times 306.25 \times 32 = 3.1416 \times 9800 = 30787.36 \, \text{cm}^3$$

The volume of one cone is:

$$V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \left( \frac{4}{2} \right)^2 \times 7 = \frac{1}{3} \pi \times 2^2 \times 7 = \frac{1}{3} \pi \times 4 \times 7 = \frac{28\pi}{3} \approx 29.3215 \, \text{cm}^3$$

The number of cones that can be filled is:

$$\text{Number of cones} = \frac{V_{\text{cylinder}}}{V_{\text{cone}}} = \frac{30787.36}{29.3215} \approx 1050$$