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 persons that can be served in this way is :

1. 950

2. 1000

3. 1050

4. 1100

In ice-cream cylinder,

Radius of cylinder, R = $\dfrac{\text{diameter}}{2} = \dfrac{35}{2}$ = 17.5 cm

Height of cylinder, H = 32 cm

In each ice-cream cone,

Radius of cone part, r = $\dfrac{\text{diameter}}{2} = \dfrac{4}{2}$ = 2 cm

Height of cone, h = 7 cm

Let the number of children who get ice-cream cone be n.

Volume of cylinder = n × Volume of ice-cream cone

$\therefore π\text{R}^2\text{H} = \text{n} \times \dfrac{1}{3}π\text{r}^2\text{h} \\[1em] \Rightarrow 3 \times \text{R}^2\text{H} = \text{n} \times \text{r}^2\text{h} \\[1em] \Rightarrow 3 \times 17.5^2 \times 32 = \text{n} \times 2^2 \times 7 \\[1em] \Rightarrow 3 \times 306.25 \times 32 = \text{n} \times 4 \times 7 \\[1em] \Rightarrow 29400 = \text{n} \times 28 \\[1em] \Rightarrow \text{n} = \dfrac{29400}{28} \\[1em] \Rightarrow \text{n} = 1050.$

Hence, option 3 is the correct option.