If the radius of a sphere is increased by 10%, then the volume will be increased by :
A. 33.1%
B. 30%
C. 50%
D. 10%
Answer: Option A
Solution(By Examveda Team)
If R is the radius of sphere, volume of the sphere = $$\frac{4}{3}\pi {R^3}$$When radius of sphere is increased by 10%
New volume :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {1.1R} \right)^3} \cr & = \frac{4}{3}\pi {R^3}\left( {1.331} \right) \cr} $$
Difference :
$$\eqalign{ & = \frac{4}{3}\pi {R^3}\left( {1.331} \right) - \frac{4}{3}\pi {R^3} \cr & = \frac{4}{3}\pi {R^3}\left( {1.331 - 1} \right) \cr & = \frac{4}{3}\pi {R^3}\left( {0.331} \right) \cr} $$
Increase % :
$$\eqalign{ & = \frac{{\frac{4}{3}\pi {R^3}\left( {0.331} \right)}}{{\frac{4}{3}\pi {R^3}}} \times 100 \cr & = 33.1\% \cr} $$
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
Join The Discussion