# Find the side of a cube whose volume is 24389 216 m 3 . - Mathematics

Sum

Find the side of a cube whose volume is$\frac{24389}{216} m^3 .$

#### Solution

Volume of a cube with side s is given by:

$V = s^3$

$\therefore s = \sqrt[3]{V}$

$= \sqrt[3]{\frac{24389}{216}}$

$= \frac{\sqrt[3]{24389}}{\sqrt[3]{216}}$

$= \frac{\sqrt[3]{29 \times 29 \times 29}}{\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3}}$   (By prime factorisation)

$= \frac{29}{2 \times 3}$

$= \frac{29}{6}$

Thus, the length of the side is $\frac{29}{6} m$ .

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.4 | Q 12 | Page 30