Painting Surface Area of Sliced Sphere

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.

  1. A.

    2.2 liters

  2. B.

    2.5 liters

  3. C.

    3.0 liters

  4. D.

    4.0 liters

  5. E.

    None of the above

Answer

D

Explanation

The surface area of a solid sphere of radius rr is 4πr24\pi r^2. It takes 2 liters to paint 4πr24\pi r^2.

When sliced into 4 identical pieces (quarter spheres), 4 circular plane surfaces passing through the center are exposed, each of area πr2\pi r^2. Total area of these 4 exposed circular faces =4×πr2=4πr2= 4 \times \pi r^2 = 4\pi r^2.

So total surface area of the 4 pieces =4πr2+4πr2=8πr2= 4\pi r^2 + 4\pi r^2 = 8\pi r^2.

Since 4πr24\pi r^2 requires 2 liters, 8πr28\pi r^2 will require 2×2=42 \times 2 = 4 liters.

Option D is correct.

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