mensuration area volumes Model Questions & Answers, Practice Test for ibps so prelims 2023
ibps so prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Quadratic Equations
In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians. Which one of the following is correct?
Answer: (a)
The area of a rectangle lies between 40 $cm^2$ and 45 $cm^2$. If one of the sides is 5 cm, then its diagonal lies between
Answer: (c)
Here, Area of Rectangle lies between 40$cm^2$ and 45$cm^2$
Given that one sides = 5cm.
Area of Rectangle = 5 × second sides
Now, If Area = 40$cm^2$
then, 40 = 5 × second sides
∵ second sides = 8cm.
Again, If Area = 45$cm^2$
45 = 5 × second sides.
∵ Second sides = 9cm.
it means that second sides varies. between 8 cm to 9 cm.
Let diagonal = d
⇒ $√{8^2 + 5^2} < d < √{5^2 + 9^2}$
⇒ $√{64 + 25} < d < √{25 + 81}$
⇒ $√{87} < d < √{106}$
⇒ $√{81} < √{89} < d < √{106} < √{121}$
⇒ $√{81} < d < √{121}$
⇒ 9cm < d < 11cm.
If AB and CD are two diameters of a circle of radius r and they are mutually perpendicular, then what is the ratio of the area of the circle to the area of the ΔACD?
Answer: (c)
Required ratio = ${\text"Area of circle"}/{\text"Area of ΔACD"}$
= ${πr^2}/{1/2 × 2r × r}$ = π
In a ΔABC, ∠B = 90° and ∠C = 2 ∠A, then what is $AB^2$ equal to?
Answer: (c)
Given, In ΔABC
∠C = 2∠A
∠B = 90°
∠A + 90° + 2∠A = 180°
∠3A = 180° – 90° = 90°
∠A = ${90°}/3$ = 30°
∴ ∠C = 2 × 30° = 60°
sin 30° = ${BC}/{AC}$
$1/2 = {BC}/{AC} ⇒ BC = 1/2$ AC
Now, sin 60° = ${AB}/{AC} ⇒ √3/2 = {AB}/{AC}$
AB = $√3/2$ AC ... (ii)
Squaring on both sides.
$AB^2 = 3/4 AC^2$, Now putting the value of AC.
$AB^2 = 3/4 × 4 BC^2 ⇒ AB^2 = 3BC^2$
In the given figure, A and B are end points of diameter of a circle with centres at P and C is a point on the circumference of the circle such that ∠ABC = 35°, then what is ∠PCA?
![mensuration area and volume aptitude mcq 24 43](https://careericons.com/adminicon/bunch/images/mensuration-area-and-volume-aptitude-mcq-24-43.png)
Answer: (d)
PC = PB (radii of circle)
∠PBC = ∠PCB
(angles opposite to equal sides)
⇒ ∠PCB = 35°
and ∠ACB = 90°
(angle in semi-circle)
⇒ ∠PCA + ∠PCB = 90°
⇒ ∠PCA = 90° – 35° = 55°
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