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Volume left in rectangular box

CMAT 2019 · Quantitative Techniques & Data Interpretation · Easy · Mensuration

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A rectangular box of width(aa), length(bb), and height(cc) has a solid cylinder of height 'cc' and of diameter 'aa' placed within it. If a=6a = 6, b=8b = 8 and c=10c = 10, how much volume is left in the rectangular box?

  1. A.

    480−180π480 - 180\pi

  2. B.

    240−96π240 - 96\pi

  3. C.

    380−90π380 - 90\pi

  4. D.

    480−90π480 - 90\pi

Answer

D

Explanation

Volume of box =a×b×c=6×8×10=480= a \times b \times c = 6 \times 8 \times 10 = 480. Radius of cylinder r=a/2=3r = a/2 = 3, height =c=10= c = 10. Volume of cylinder =πr2c=π×32×10=90π= \pi r^2 c = \pi \times 3^2 \times 10 = 90\pi.

Volume left =480−90π= 480 - 90\pi.

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