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## Geometry and Mensuration: Level 1 Test 1

Congratulations - you have completed Geometry and Mensuration: Level 1 Test 1. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
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 Question 1
The area of circle is seven times the numerical value of its circumference. What is the circumference of the circle?
 A 616 units B 132 units C 88 units D Cannot be determined
Question 1 Explanation:
Let the radius of the circle be r units.
$\begin{array}{l}\pi {{r}^{2}}=7\times 2\pi r\\=>r=14\\=>2\pi r=\frac{2\times 22}{7}\times 14=88units\\Correct\,\,option\,\,is\,\,(c)\end{array}$
 Question 2
AD is the median of a triangle ABC and O is the centroid such that AO= 10 cm. The length of OD in cm is
 A 4 B 5 C 6 D 8
Question 2 Explanation:

AO = 10 cm. Therefore ,
AD= 3/2 AO = 15 cm.
OD = 1/3 AD = 1/3 x 15 cm = 5 cm.
 Question 3
What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs.10 per square metre?
 A Rs.3, 400/- B Rs.1, 700/- C Rs.3, 440/- D Cannot be determined
Question 3 Explanation:
Let the length be l and breadth be b units.
Area of the boundary= lb+2(l+b)+4-lb
= 2(l+b) +4 =344
The total cost = 344 x 10 = Rs. 3440
Correct option is (c)
 Question 4
If ΔABC is an isosceles triangle with ∠C= 90o and AC= 5cm, then AB is:
 A 5 cm B 10 cm C 5√2cm D 2.5 cm
Question 4 Explanation:
$\begin{array}{l}AB=\sqrt{2\times {{5}^{2}}}\\AB=5\sqrt{2}\\The\,\,correct\,\,option\,\,is\,\,c\end{array}$
 Question 5
The ratio of the length and the breadth of a rectangular plot is 6:5 respectively. If the breadth of the plot is 34 metres less than the length, what is the perimeter of the rectangular plot?
 A 374 metres B 408 metres C 814 metres D 748 metres
Question 5 Explanation:
$\displaystyle \begin{array}{l}Let\text{ }the\text{ }plot\text{ }be\text{ }of\text{ }length\text{ }and\text{ }breadth\text{ }6x\text{ }and\text{ }5x\text{ }units\text{ }resp.\\6x-5x\text{ }=\text{ }34.\\Thus\text{ }the\text{ }perimeter\text{ }=\text{ }2x\text{ }\left( 5x+6x \right)\text{ }\times ~34\text{ }=\text{ }22\times 34\text{ }=748\text{ }cm.\end{array}$
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