If the radius of a circle is decreased by 50%, find the percentage decrease in i

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Question
If the radius of a circle is decreased by 50%, find the percentage decrease in its area.
Options
A. 55%
B. 65%
C. 75%
D. 85%

Correct Answer

75%

Explanation

Let original radius = R.

New radius = $\frac{50}{100} R$ = $\frac{50}{100} R$

Original area = $\frac{R}{2}$ and new area = ${?R}^{2}$

$\frac{3 {?R}^{2}}{4} * \frac{1}{{?R}^{2}} * 100$

Decrease in area = $? {(\frac{R}{2})}^{2} = \frac{{?R}^{2}}{4}$ = 75%

Area problems

Search Results

1. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
Options
A. Rs. 456
B. Rs. 458
C. Rs. 558
D. Rs. 568

4. Two circles touch each other at point X. A common tangent touch them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA= 16 cm, then what is the value (in cm) of YZ?
Options
A. 18
B. 24
C. 16
D. 32

9. In a wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course is shown. Find the perimeter of the course
Options
A. 32
B. 42
C. 62
D. 92

10. If the ratio of area of rectangle to its perimeter is 60:11. And length and breadth are in the ratio 6 : 5. Find length of rectangle.
Options
A. 40 units
B. 30 units
C. 13 units
D. 24 units

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