Question

A hemispherical vessel of radius 30 cm is full of mixture to prepare kulfis. Kulfi-moulds are right circular cones of 5 cm diameter at base, having a height of 10 cm. Maximum how many kulfis can be prepared by filling the moulds up to the brim?

• A. 432
• B. 864
• C. 536
• D. 216

Hint:

To compare volumes, always use the correct formulas and simplify calculations carefully to avoid errors.

Answer 1

The Correct Option is B

Step 1: Calculating the volume of the hemispherical vessel. - The formula for the volume of a hemisphere is: \[ V = \frac{2}{3} \pi r^3 \] - Given \( r = 30 \) cm: \[ V = \frac{2}{3} \pi (30)^3 = \frac{2}{3} \pi (27000) = 18000\pi \text{ cm}^3 \]
Step 2: Calculating the volume of one kulfi-mould. - The formula for the volume of a cone is: \[ V = \frac{1}{3} \pi r^2 h \] - Given \( r = \frac{5}{2} = 2.5 \) cm and \( h = 10 \) cm: \[ V = \frac{1}{3} \pi (2.5)^2 (10) = \frac{1}{3} \pi (6.25) (10) = \frac{62.5}{3} \pi \text{ cm}^3 \]
Step 3: Finding the number of kulfis that can be made. \[ \frac{\text{Total Volume}}{\text{Volume of one kulfi}} = \frac{18000\pi}{\frac{62.5}{3} \pi} \] \[ = \frac{18000 \times 3}{62.5} = \frac{54000}{62.5} = 864 \] Thus, the correct answer is option B (864).