Question : The total number of spherical bullets, each of 5 dm in diameter, that can be made by utilising the maximum of a rectangular block of lead with 11 m of length, 10 m of breadth, and 5 m of width is: (Assume that $\pi =\frac{22}{7}$)
Option 1: equal to 8800
Option 2: less than 8800
Option 3: equal to 8400
Option 4: greater than 9000
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Correct Answer: equal to 8400
Solution :
The volume of the rectangular block, $V_1$ = length × width × height
Length is $11 \;\mathrm{m}$, width is $10 \;\mathrm{m}$, and height is $5 \;\mathrm{m}$.
$V_1 = 11×10 × 5 = 550 \text{ m}^3$
The volume of a sphere, $V_2=\frac{4}{3}\pi r^3$
The diameter of each bullet $=5 \;\mathrm{dm}=0.5 \;\mathrm{m}$
The radius of each bullet $=0.25 \;\mathrm{m}$
So, $V_2 = \frac{4}{3}\pi (0.25)^3 = \frac{1}{6}\pi \text{ m}^3=\frac{11}{168} \text{ m}^3$
The number of bullets $ = \frac{V_1}{V_2} = \frac{550}{\frac{11}{168}}=8400$
Hence, the correct answer is 'equal to 8400'.
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