Question

The given figure shows the portion of a rectangular pyramid that is to be cut off to make a perfume bottle.
If the top $40mm$ of the pyramid is cut off and its base area is $600sqmm$, then what percent of the volume of the original bottle was removed? Round off the answer to the nearest two-decimal places.
(Assume that the thickness of the perfume bottle is negligible.)

• A. $15.6$%
• B. $2.1$%
• C. $1.65$%
• D. $1.56$%

Answer 1

The correct option is D $1.56$%

Volume of the whole pyramid, $V_1=\frac{80\times 120\times 160}{3}=512,000cumm$

Volume that is to be cut off, $V_2=\frac{600\times 40}{3}=8,000cumm$

Percent of the volume of the original bottle that was removed
$=\frac{V_2}{V_1}\times 100$%

$=\frac{8,000}{512,000}\times 100$%

$=1.5625$ %

$\simeq 1.56$%