 This is an assessment test.
 To draw maximum benefit, study the concepts for the topic concerned.
 Kindly take the tests in this series with a predefined schedule.
Geometry and Mensuration: Level 1 Test 6
Congratulations  you have completed Geometry and Mensuration: Level 1 Test 6.
You scored %%SCORE%% out of %%TOTAL%%.
You correct answer percentage: %%PERCENTAGE%% .
Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1 
A solid metallic sphere of radius r is converted into a solid right circular cylinder of radius R. If the height of the cylinder is twice the radius of the sphere, then
R = r  
$ \displaystyle R=\text{ }r\sqrt{\frac{2}{3}}$  
$ \displaystyle R=\sqrt{\frac{2r}{3}}$  
$ \displaystyle R=\frac{2r}{3}$ 
Question 1 Explanation:
$ \begin{array}{l}\frac{4}{3}\pi {{r}^{3}}=\pi {{R}^{2}}\times 2r\\=>\frac{2}{3}{{r}^{2}}={{R}^{2}}\\=>R=\sqrt{\frac{2}{3}r}\end{array}$
Question 2 
The radius of a circle is twice the side of a square of area 196 sq.cm. Length of a rectangle is twice diameter of the circle. What is the perimeter of the rectangle if its breadth is haft the length of the rectangle?
244 cm  
168 cm  
336 cm  
Cannot be determined 
Question 2 Explanation:
Side of the square = 14 cm.
Radius of the circle = 28 cm.
Diameter of the circle = 56 cm.
Length of the rectangle = 112 cm.
Breadth =1/2 x 112 = 56cm
Perimeter of the rectangle = 2(112+56) = 336 cm.
Correct option is (c)
Radius of the circle = 28 cm.
Diameter of the circle = 56 cm.
Length of the rectangle = 112 cm.
Breadth =1/2 x 112 = 56cm
Perimeter of the rectangle = 2(112+56) = 336 cm.
Correct option is (c)
Question 3 
The smallest side of a right angled triangle is 6 cm, and second largest side is 8 cm. The side of a square is thrice the largest side of the triangle. What is the length of the diagonal of the square?
30âˆš2 cm
 
60âˆš2 cm  
30 cm.  
Cannot be determined 
Question 3 Explanation:
\[\begin{align}
& The\,\,third\,\,side=\sqrt{({{8}^{2}}+{{6}^{2}})}=\sqrt{(64+36)}=10 \\
& The\,\,side\,\,of\,\,the\,\,square=3\times 10=30\,cm \\
& The\,\,length\,\,of\,\,the\,\,diagonal\,\,is\,\,30\sqrt{2}\,cm \\
& Correct\,\,option\,\,is\,\,(a) \\
\end{align}\]
Question 4 
In the figure there are two rectangles ABCD and DEBG, each of length 7 cm and width 3 cm. The area of shaded region, in cm, is approximately
12  
10  
8  
4

Question 4 Explanation:
The shaded region covers roughly half of the rectangle.
A bit more accurate measurement will be slightly more than half the rectangle.
Thus the shaded region >1/2 x 7x3 = 10.5 cm^{2}
Thus the closest option greater than 10.5
A bit more accurate measurement will be slightly more than half the rectangle.
Thus the shaded region >1/2 x 7x3 = 10.5 cm^{2}
Thus the closest option greater than 10.5
Question 5 
Height of a cylindrical jar is decreased by 36%. By what percent must the radius be increased so that there is no change in its volume?
25
 
35  
36  
40 
Question 5 Explanation:
Let the height be h cm
The new height = .64h.
Thus for constant volume, the radius must be increased by
{(1/0.8) â€“ 1}=1.251=(0.25/1)x100 = 25%
The new height = .64h.
Thus for constant volume, the radius must be increased by
{(1/0.8) â€“ 1}=1.251=(0.25/1)x100 = 25%
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
There are 5 questions to complete.
List 