Question : The number of lead balls, each 3 cm in diameter, that can be made from a solid lead sphere of diameter 42 cm is:
Option 1: 2744
Option 2: 4722
Option 3: 7244
Option 4: 2742
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Correct Answer: 2744
Solution : Given: A solid lead sphere of diametre 42 cm. The radius of a solid sphere is 21 cm. The radius of a small sphere = $\frac{3}{2}$ = 1.5 cm. The volume of the sphere of radius $r$ is $\frac{4}{3}\pi r^3$. Let $x$ be the total number of lead balls that can be made. According to the question, ⇒ $\frac{4}{3}\times\pi \times(21)^3=x\times\frac{4}{3}\times\pi \times(1.5)^3$ ⇒ $x=\frac{21\times 21\times 21\times 1000}{15\times 15\times 15}=7\times 7\times 7\times 2\times 2\times 2=2744$ Hence, the correct answer is 2744.
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Question : A thousand solid metallic spheres of 6 cm diameter each are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is:
Option 1: 30
Option 2: 90
Option 3: 45
Option 4: 60
Question : The number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 90 cm and diameter 4 cm is:
Option 1: 10
Option 2: 14
Option 3: 16
Option 4: 13
Question : How many spherical lead shots each of diameter 8.4 cm can be obtained from a rectangular solid of lead with dimensions 88 cm, 63 cm, and 42 cm?(Take $\left.\pi=\frac{22}{7}\right)$
Option 1: 920
Option 2: 750
Option 3: 650
Option 4: 860
Question : A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are $\frac{3}{2}$ cm and 2 cm, respectively. Find the diameter of the third ball.
Option 1: 2.1 cm
Option 2: 3.3 cm
Option 3: 3 cm
Option 4: 2.5 cm
Question : Three solid metallic spheres of radii 1 cm, 6 cm, and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere formed is:
Option 1: 9.0 cm
Option 2: 5.9 cm
Option 3: 7.7 cm
Option 4: 8.5 cm
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