Molten Sphere Surface Area Increase

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

A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:

  1. A.

    1000 times

  2. B.

    100 times

  3. C.

    10 times

  4. D.

    No change

  5. E.

    None of the above

Answer

E

Explanation

Large sphere volume = 43πR3=43π(103)\frac{4}{3}\pi R^3 = \frac{4}{3}\pi (10^3). Small spheres radius rr: 1000×43πr3=43π(103)  ⟹  r=11000 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (10^3) \implies r = 1 cm. Original surface area = 4π(102)=400π4\pi (10^2) = 400\pi. Total new surface area = 1000×4π(12)=4000π1000 \times 4\pi (1^2) = 4000\pi. Increase in surface area = 4000π−400π=3600π4000\pi - 400\pi = 3600\pi, which is an increase of 9 times (or 10 times the original value, increased by 900%). Neither 1000, 100, 10, nor no change is correct. Hence, None of the above.

Related Mensuration questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace