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A sphere of diameter $10$ cm weighs $44$ kg. The weight of a sphere of the same material whose diameter is $6$ cm is

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2.64

1.58 4

0.9504

\frac{4}{3} (0.9504) kg

answer is C.

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Detailed Solution

Given the diameter of sphere is 10 cm and weight = 44kg.
Assume the weight of the sphere of diameter

6

cm be

x

kg and density of the material be

d

gm/c.c.
The formula for the volume of sphere is given by,
Volume of a sphere

= 43 π r 3

, where r is the radius. Also, we know that,

Mass = Volume × Density

So, after substituting the value of all the dimensions in the formula we get,

∴ \frac{x}{4.4} = \frac{\frac{4}{3 π} \times 3^{3} \times d}{\frac{4}{3 π} \times 5^{3} \times d}

⟹ x = \frac{4.4 \times 27}{125}

⟹ x = 0.9504 kg

Therefore, the weight of a sphere of the same material whose diameter is

6

cm is

0.9504

kg.
Hence, option (3) is correct.

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