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%
Answer: Option C
Solution(By Examveda Team)
Let original edge = aThen, original volume = a3
New edge :
$$\eqalign{ & = \frac{{150}}{{100}}a \cr & = \frac{{3a}}{2} \cr} $$
New volume :
$$\eqalign{ & = {\left( {\frac{{3a}}{2}} \right)^3} \cr & = \frac{{27{a^3}}}{8} \cr} $$
Increase in volume :
$$\eqalign{ & = \left( {\frac{{27{a^3}}}{8} - {a^3}} \right) \cr & = \frac{{19{a^3}}}{8} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{19{a^3}}}{8} \times \frac{1}{{{a^3}}} \times 100} \right)\% \cr & = 237.5\% \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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