mensuration area volumes Model Questions & Answers, Practice Test for ibps po prelims 2023
ibps po prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Surds & Indices
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
In a right angled ΔABC, ∠C = 90° and CD is perpendicular to AB. If AB × CD = CA × CB, then $1/{CD}^2$ is equal to
Answer: (a)
In ΔABC
CD ⊥ AB
and AB × CD = CA × CB .... (i)
In ΔCDB
$BC^2 = BD^2 + CD^2$ ... (ii)
$CD^2 = BC^2 – BD^2$
From eq. (i) and (ii)
$1/{CD^2} = 1/{BC^2} - 1/{CA^2}$
ABCD is a parallelogram with AB and AD as adjacent sides. If ∠A = 60° and AB = 2AD, then the diagonal BD will be equal to
Answer: (c)
Using cosine law
cos A = ${AD^2 + AB^2 - BD^2}/{2.AD.AB}$
⇒ cos 60° = ${AD^2 + (2AD)^2 - BD^2}/{2.AD.2AD}$
⇒ $1/2 = {AD^2 + 4AD^2 - BD^2}/{4AD^2}$
⇒ $2AD^2 = 5AD^2 – BD^2$
⇒ $BD^2 = 5AD^2 – 2AD^2$
⇒ BD = $3AD^2$
⇒ BD = $√3$ AD
So, option (c) is correct.
A tent of a circus is made of canvas and is in the form of right circular cylinder and right circular cone above it. The height and diameter of the cylindrical part of the tent are 5 m and 126 m respectively. The total height of the tent is 21 m. How many square metres of canvas are used ?
Answer: (d)
Canvas used = $CSA_{cylinder} + CSA_{cone}$
= 2πrh + πrl
= 1980 + ${22}/7 × 63 × 65 = 14850 m^2$
In the figure given above, O is the centre of the circle. What is ∠AOC?
Answer: (d)
Join OB. OA = OB = OC
Then,
∠OAB = ∠OBA = 20°
∠OCB = ∠OBC = 30°
∠ABC = 50°
We know that ∠ABC = $1/2$ ∠AOC
∴ ∠AOC = 2 ∠ABC = 2 × 50° = 100°
The radius and height of a right circular cone are in the ratio 3 : 4 and its volume is 96π $cm^3$ . What is its lateral surface area?
Answer: (d)
Let radius and height of a cone be r and h
∵ $r/h = 3/4$
Volume of cone = $1/3 πr^2 h$
∴ 96π = $1/3 π × r^2 × {4r}/3$
⇒ $r^3 = {96 × 3 × 3}/4$ = 216 ⇒ r= 6 cm
and h = 8 cm
∴ Lateral surface area
= πr$√{r^2 + h^2}$
= π × 6$√{36 + 64}$
= 60π sq cm
ibps po prelims 2023 IMPORTANT QUESTION AND ANSWERS
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