Question : A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7 cm. The ratio of the total surface areas of the rod to the sphere is:
Option 1: 3 : 1
Option 2: 1 : 3
Option 3: 7 : 3
Option 4: 3 : 7
Correct Answer: 7 : 3
Solution :
Given: Radius of the sphere ($R$) = 2.1 dm = 21 cm
Height of the rod = 7 cm
Let the radius of the rod be $r$ cm.
Now,
The volume of the rod = volume of the sphere
$⇒\pi r^2 h=\frac{4}{3}\pi R^3$
$⇒r^2\times 7 = \frac{4}{3}\times21\times21\times21$
$\therefore r = 42$
The ratio of the total surface area of the rod to the sphere
$=2\pi r(h+r):4\pi R^2$
$=2 × 42 × (42 + 7): 4 × 21 × 21$
$=2 × 42 × 49: 4 × 21 × 21$
$=7: 3$
Hence, the correct answer is 7 : 3.
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