Practice | Hashtable

1. By what percent the volume of a cube increases if the length of each edge was increased by 50%

A. 50%

B. 125%

C. 237.5%

D. 273.5%

Solution:

Let original edge = a
Then, original volume = a³
New edge :

\begin{aligned} = \frac{150}{100} a \\ = \frac{3 a}{2} \end{aligned}

New volume :

\begin{aligned} = {(\frac{3 a}{2})}^{3} \\ = \frac{27 a^{3}}{8} \end{aligned}

Increase in volume :

\begin{aligned} = (\frac{27 a^{3}}{8} - a^{3}) \\ = \frac{19 a^{3}}{8} \end{aligned}

∴ Increase % :

\begin{aligned} = (\frac{19 a^{3}}{8} \times \frac{1}{a^{3}} \times 100) % \\ = 237.5 % \end{aligned}

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