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Bakery Conical Equipment Cream Writing

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Mensuration

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Suresh, who runs a bakery, uses a conical shaped equipment to write decorative labels (e.g., Happy Birthday etc.) using cream. The height of this equipment is 7 cm and the diameter of the base is 5 mm. A full charge of the equipment will write 330 words on an average. How many words can be written using three fifth of a litre of cream?

  1. A.

    45090

  2. B.

    45100

  3. C.

    46000

  4. D.

    43200

  5. E.

    None of the above.

Answer

E

Explanation

Cone dimensions: height h=7h = 7 cm, base radius r=0.25r = 0.25 cm. Volume of cone = 13πr2h=13×227×(0.25)2×7=0.45833 cm3\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times (0.25)^2 \times 7 = 0.45833\text{ cm}^3. 1 charge (0.45833 cm30.45833\text{ cm}^3) writes 330 words. Cream available = 35\frac{3}{5} litre = 600 cm3600\text{ cm}^3. Words written = 600×3300.45833≈432,000600 \times \frac{330}{0.45833} \approx 432,000 words. Since 432,000 is not in A-D (option D says 43200), option E (None of the above) is correct.

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