Question

If a rectangular box of length 14 cm, breadth 22 cm, and height 14 cm is converted into a cylindrical box whose height is 7 cm, then find the radius of the converted cylindrical box.

• A. $13cm$
• B. $14cm$
• C. $15cm$
• D. $16cm$

Answer 1

The correct option is B $14cm$

Given:
Length(L), breadth(B), and height(H) of the rectangular box are 14 cm, 22 cm and 14 cm respectively.
Height of the cylindrical box(h) = 7 cm

Given,
Volume of the rectangular box = Volume of the cylindrical box
$\Rightarrow L\times B\times H=\pi r^{2}h$
$\Rightarrow 14\times 22\times 14=\frac{22}{7}\times r^2\times 7$
$\Rightarrow 14\times 14=r^2$
$\Rightarrow r=\sqrt{14\times 14}$
$\Rightarrow r=14cm$