Question

How many quarters equal the volume of a piece of paper? A quarter has a diameter of \[0.9375\;inches\] , a thickness of $ 0.0625\;inches $ .The piece of a paper is $ 10.5 $ by $ 8(inches) $ , and a thickness of $ 0.0025 $.

Answer 1

Hint: To solve the problem we should know about the following term.
Volume: volume is the quantity of three – dimensional space enclosed by a closed surface, for example, the space that a substance (solid, gas, liquid, or plasma) or shape occupies or contains.

Complete step by step solution:
As given in the question
The quarter has,
Diameter \[ = 0.9375\;inches\]
Thickness $ = 0.0625\;inches $
Piece of paper $ = 10.5 \times 8(inches) $
Thickness $ = 0.0025 $
(volume of paper / volume of quarter) gives the number of quarters.
Volume of paper
  $ {V_p} = {l_p} \times {b_p} \times {h_p} = 10.5 \times 8 \times 0.0025 = 0.21\,inc{h^3} $
Volume of quarter
  $ {V_q} = \pi {r_q}^2{h_q} = \pi \times {\left( {\dfrac{{0.9375}}{2}} \right)^2} \times 0.0625 \approx 0.0427inc{h^3} $
By using formula:
No. of quarters $ = \dfrac{{volume\,of\,paper}}{{volume\,of\,quarter}} $
By keeping the value,
  $ \Rightarrow \dfrac{{0.21}}{{0.0427}} = 4.918 $
Hence, Number quarters equal the volume of a piece of paper is $ 4.918 $
but since the number has to be a discrete value we take it as 5.
So, the correct answer is “5”.

Note: The volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However sometimes one substance dissolves in the order and in such cases the combined volume is not additive.