- 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 pre-defined 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?
30√2 cm | |
60√2 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 cm2
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 cm2
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) – 1}=1.25-1=(0.25/1)x100 = 25%
The new height = .64h.
Thus for constant volume, the radius must be increased by
{(1/0.8) – 1}=1.25-1=(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 |
