aptitude mensuration mcq pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (b)

Let r be the radius of cylindrical block, then height will be 2r.

Volume of block = π$(r^2) (2r) = 2πr^3$

A sphere of maximum possible volume is carved out whose radius will be r.

∴ Volume of sphere = $4/3 πr^3$

∴ Volume of utilised wood = $4/3 πr^3$

and volume of wasted wood = $2πr^3 - 4/3 πr^3$

= ${6πr^3 - 4 πr^3}/3 = {2πr^3}/3$

∴ Required ratio = $4/3 πr^3 : 2/3 πr^3 = 2 : 1$

Answer: (a)

S = $l^3 + b^3 + h^3$

and V = lbh

Now, S – 3V = $l^3 + b^3 + h^3$ – 3lbh

= (l + b + h) $(l^2 + b^2 + h^2$ – (lb + bh + lh))

= 22 (196 – 144) = 1144 $cm^2$

Answer: (b)

Given, BD = 2DC

∴ BC + CD = 2DC ⇒ BC = CD ...(i)

In ΔABC,

$AC^2 = AB^2 + BC^2$ ...(ii)

In ΔABD, $AD^2 = AB^2 + BD^2$ ...(iii)

Subtracting Eq. (ii) from Eq (iii),

we get $AD^2 – AC^2 = BD^2 – BC^2$ = (BD – BC) (BD + BC)

= CD (2CD + CD) = $3CD^2$

$AC^2 = AD^2 – 3CD^2$

Answer: (c)

Given, AO : OC = BO : OD

and AB= 30 cm and CD = 40 cm 40 cm

∴ ΔAOB ~ ACOD ⇒ ${OA}/{OC} = {AB}/{CD} = 3/4$

∴ ∠OAB= ∠OCD and ∠OBA = ∠ODC

It means DC || AB. So, it is a trapezium.

Area of quadrilateral ABCD = $1/2$ (AB + CD) × AE

⇒ 1050 = $1/2$ (30 + 40) × AE

⇒ AE = 30 cm

Also,∠BAE = 90°

Also ∠BAE = 90°, AE = AB = 30 cm

∴ ∠AEB = ∠ABE = 45°

Answer: (a)

We know that x + y + ${xy}/{100}$

Here x = 6% and y = 6%

= 6 + 6 + ${6 × 6}/{100}$

= 12 + .36 = 12.36%