Question

An ice-cream pot has a right circular cylindrical shape. The radius of the base is 12 cm and the height is 7 cm. This pot is completely filled with ice-cream. The entire ice-cream is given to students in the form of right circular cones having diameter 4 cm and height 3.5 cm. If each student is given one cone, how many students can be served?

Hint:

When solids are melted and recast, their volumes remain equal. Always use $\text{Volume of solid 1} = \text{Volume of solid 2}$ for such problems.

Answer 1

Step 1: Find the volume of the cylindrical pot.
\[ V_1 = \pi r_1^2 h_1 \] Given $r_1 = 12$ cm and $h_1 = 7$ cm, \[ V_1 = 3.14 \times 12^2 \times 7 = 3.14 \times 144 \times 7 = 3165.12 \, \text{cm}^3 \] Step 2: Find the volume of one ice-cream cone.
Diameter of cone = 4 cm, so radius $r_2 = 2$ cm, and height $h_2 = 3.5$ cm.
\[ V_2 = \frac{1}{3} \pi r_2^2 h_2 \] \[ V_2 = \frac{1}{3} \times 3.14 \times 2^2 \times 3.5 = \frac{1}{3} \times 3.14 \times 4 \times 3.5 = 14.66 \, \text{cm}^3 \] Step 3: Find the number of students.
\[ \text{Number of students} = \frac{V_1}{V_2} = \frac{3165.12}{14.66} \approx 216 \] Step 4: Conclusion.
Hence, 216 students can be served one cone each.
Correct Answer: 216 students