mensuration area volumes Model Questions & Answers, Practice Test for ibps po prelims 2023

Answer: (b)

Number of spheres

= ${\text"Volume of a solid sphere with radius 4 cm"}/{\text"Volume of a solid sphere with radius 2 cm"}$

= ${4/3 π (4)^3}/{4/3 π (2)^3} = {(2)^6}/{(2)^3} = (2)^3$ = 8

Answer: (b)

Answer: (c)

Given, ∠BAD = 60°, ∠ADC = 105°

in cycle quadrilateral ABCD,

∠1 + ∠3 = 180°

⇒ ∠3 = 180° – 60° = 120°

Now,∠BCD + ∠DCP = 180°

(straight line)

⇒ ∠DCP = 180° – 120° = 60°

and, ∠ADC + ∠CDP = 180°

(straight line)

⇒ 105° + ∠CDP = 180° ⇒ ∠CDP = 75°

Now in ΔCPD,

∠DCP + ∠CDP + ∠DPC = 180°

⇒ 60° + 75° + ∠DPC = 180°

∴ ∠DPC = 180° – 135° = 45°

Answer: (c)

Since, ∠ADB = $1/2$ ∠AOB = 50°

In ΔDPA, ∠DAP + ∠ADP + ∠DPA = 180°

⇒ 30° + 50° + ∠DPA= 180° ⇒ ∠DPA = 100°

Also, DPB be a straight line.

∴ ∠DPA + ∠APB = 180°

⇒ ∠APB = 180° – 100° = 80°

Answer: (d)

Area of Largest square = $d^2/2$

Where ‘d’ is the diameter of the circular disk ∼ and d = 2r = 2

Hence, Area = ${(2)^2}/2$ = 2sq.4 units.