If the radius of a circle is increased by 75%, then its circumference will increase by :
A. 25%
B. 50%
C. 75%
D. 100%
Answer: Option C
Solution(By Examveda Team)
Let original radius be R cmThen, original circumference = $$2\pi r$$ cm
New radius :
$$\eqalign{ & = \left( {175\% {\text{ of }}R} \right)cm \cr & = \left( {\frac{{175}}{{100}} \times R} \right)cm \cr & = \frac{{7R}}{4}\,cm \cr} $$
New circumference :
$$\eqalign{ & = \left( {2\pi \times \frac{{7R}}{4}} \right)cm \cr & = \frac{{7\pi R}}{2}\,cm \cr} $$
Increase in circumference :
$$\eqalign{ & = \left( {\frac{{7\pi R}}{2} - 2\pi R} \right)cm \cr & = \frac{{3\pi R}}{2}\,cm \cr} $$
Increase % :
$$\eqalign{ & = \left( {\frac{{3\pi R}}{2} \times \frac{1}{{2\pi R}} \times 100} \right)\% \cr & = 75\% \cr} $$
Related Questions on Area
A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
E. None of these
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
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