A hollow spherical metallic ball has an external diameter 6 cm and is 1/2 cm thick. Find the volume of the metal used in the ball.

Correct Answer is : 4723 cm3472/3\,{cm}³4732cm3

Correct Answer is : 4723 cm3472/3\,{cm}³4732cm3

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Volumes Practice Test 4

Question : 14 of 16

Marks: +1, -0

\frac{1}{2}

Solution:

Concept:

Volume of metal in a hollow sphere is the difference between the outer and inner spherical volumes.

Explanation:

External radius

R = \frac{6}{2} = 3\,\mathrm{cm}

Internal radius

r = 3 - \frac{1}{2} = \frac{5}{2}\,\mathrm{cm}

Metal volume

V = \frac{4}{3}\pi(R^3 - r^3)

Substitute values:

V = \frac{4}{3}\pi\left(3^3 - \left(\frac{5}{2}\right)^3\right)

V = \frac{4}{3}\times\frac{22}{7}\left(27 - \frac{125}{8}\right)

V = \frac{4}{3}\times\frac{22}{7}\times\frac{91}{8}

V = \frac{143}{3} = 47\frac{2}{3}\,\mathrm{cm}^3

Answer:

47\frac{2}{3}\,\mathrm{cm}^3

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