Discussion
Diameter of a solid sphere is equal to perimeter of a rectangle. Area of the rectangle is 432 \(\mathrm{cm}^{2}\). The difference between length and breadth of the rectangle is 6 cm. What will be the volume of sphere?
Answer: B
The length and breadth satisfy l x b = 432 and l - b = 6, so l = 24 cm and b = 18 cm, since 24 x 18 = 432. The perimeter is 2(24 + 18) = 84 cm, and this is the diameter of the sphere, so the radius is 42 cm.
\[ V = \tfrac{4}{3}\pi r^{3} \]
\[ V = \tfrac{4}{3}\times\tfrac{22}{7}\times 42^{3} \]
\[ V = 310464\ \mathrm{cm}^{3} \]
So the volume is 310464 cm cubed, option (B). The other values do not follow from the radius of 42 cm. The perimeter of a rectangle of sides 24 and 18 is 84, and the diameter of the sphere is 84, so the radius is 42, which is used in the formula.
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