Mensuration Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 2 EXERCISES
The following question based on Mensuration topic of quantitative aptitude
- Statement I
- If AB > BC, then AB + AZ < BC + XC
- Statement II
- AZ = AY
(a) Statement I is correct and Statement II is incorrect
(b) Statement I and II are correct and Statements II is the correct explanation of Statement I
(c) Statement I and II are correct and Statement II is not the correct explanation of Statement I
(d) Statement I is incorrect and Statement II is correct
The correct answers to the above question in:
Answer: (d)
In ΔAOZ and ΔAOY,
AO = OA [common]
∠OAZ = ∠OAY [Since, OA bisect ∠A]
and ∠AZO = ∠AYO [each 90°]
∴ ΔAZO ≅ ΔAYO
So, AZ = AY [by CPCT]
Similarly, CX = CY and BX = BZ
Now, AB > BC
∴ AZ + ZB > BX + XC
AZ > XC [∵ BX = ZB]
If AB > BC, then AB + AZ > BC + XC
So, Statement I is incorrect and Statement II is correct.
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Read more model questions set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If ∠QPT = α, then what is ∠POQ equal to?
![mensuration area and volume aptitude mcq 24 112](https://careericons.com/adminicon/bunch/images/mensuration-area-and-volume-aptitude-mcq-24-112.png)
a) 90° – α
b) α
c) 2α
d) 180° – 2α
Answer »Answer: (c)
Question : 2
The length of a minute hand of a wall clock is 9 cm. What is the area swept (in $cm^2$) by the minute hand in 20 min? (take π = 3.14)
a) 67.74
b) 88.78
c) 84.78
d) 57.78
Answer »Answer: (c)
The angle made by the minute hand in 20 min = 120°
∴ The area swept by the minute hand in 20 min
= $θ/{360°} × π r^2 = ∼ {120°}/{360°} × 3.14 × 9 × 9 = 84.78 cm^2$
Question : 3
A large water tank has the shape of a cube. If 128 $m^3$ of water is pumped out, the water level goes down by 2 m. Then the maximum capacity of the tank is
a) 324 $m^3$
b) 512 $m^3$
c) 480 $m^3$
d) 256 $m^3$
Answer »Answer: (b)
Let side of cubical water tank be 'x' meter.
Capacity of tank = $x^3$
According to question
⇒ $x^3 – 128 = (x – 2).x^2$
⇒ $x^3 – 128 = x^3 – 2x^2$
⇒ $2x^2$ = 128
⇒ $x^2$ = 64
⇒ x = 8 metre
Capacity of tank $(8)^3 = 512 m^3$
So, option (b) is correct.
Question : 4
In the figure given below, what is ∠BCD equal to?
![mensuration area and volume aptitude mcq 24 122](https://careericons.com/adminicon/bunch/images/mensuration-area-and-volume-aptitude-mcq-24-122.png)
a) 80°
b) 70°
c) 75°
d) 90°
Answer »Answer: (a)
∠BAC = ∠BDC {Angle made by same chord BC in the same side}
Now, from ΔBCD, sum of angles = 180°
∠CBD + ∠BDC + ∠BCD = 180°
∴ ∠BCD = 180° – 100° = 80°
Question : 5
A hollow right circular cylindrical vessel of volume V whose diameter is equal to its height, is completely filled with water. A heavy sphere of maximum possible volume is then completely immersed in the vessel. What volume of water remains in the vessel ?
a) ${2V}/3$
b) $V/2$
c) $V/3$
d) $V/4$
Answer »Answer: (a)
As per the given condition, the radius of sphere and cylinder will be same.
Volume of cylinder = $πR^2H = πR^2 .D = 2πR^3$
(where R = Radius)
Volume of sphere $V_s = 4/3 π R^3$
⇒ = ${V_S}/V ={4/3 π R^3}/{2π R^3} = 2/3 ⇒ V_s = 2/3 V$
Question : 6
The areas of two circles are in the ratio 1 : 2. If the two circles are bent in the form of squares, then what is the ratio of their areas?
a) 1 : $√2$
b) 1 : 2
c) 1 : 3
d) 1 : 4
Answer »Answer: (b)
According to question
$A_1/A_2 = {π r_1^2}/{πr_2^2} = 1/2$
⇒ $(r_1/r_2)^2 = 1/2$ ...(i)
As, Circles are bent in the form of square then their perimeter will become equal.
$2πr_1 = 4a_1$
⇒ $a_1 = {πr_1}/2$
Similarly, $a_2 = {π r_2}/2$
∴ $A_1/A_2 = a_1^2/a_2^2 = {({π r_1}/2)^2}/{({π r_2}/2)^2} = r_1^2/r_2^2 = 1/2$[from Eq. (i)]
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