mensuration Model Questions & Answers, Practice Test for ibps clerk prelims 2024

Answer: (c)

Let the radius of cylindrical rod = r and height = 4r

∴ Required number of spherical balls

= ${\text"Volume of cylindrical rod"}/{\text"Volume of spherical balls"} = {πr^2 (4r)}/{4/3 πr^3}$ = 3

Answer: (c)

Let perimeter 4a = 20

⇒ a = 5

Volume of cube = $a^3$ = 125

Hence, pairs (20, 125), represents the perimeter of one face of a cube and volume of cube.

Answer: (c)

By using Pythagoras theorem in ΔABC.

$AC^2 = AB^2 + BC^2 = AC^2$ = 64 + 64

∴ $AC^2 = 8 √2$

ABC is isosceles right angle triangle, then

AP = PC = PB = ${AC}/2 = 4√2$

Answer: (a)

in ΔAPB

AB = ${13}/2$ cm, BP = ${12}/2$ = 6 cm

AP = ?

$AP^2 = AB^2 – BP^2$

$AP^2 = ({13}/2)^2 - ({12}/2)^2 = (5/2)^2$

AP = $5/2$

in ΔAQD

$AQ^2 = AD^2 – DQ^2$

= $({13}/2)^2 - (5/2)^2 = ({12}/2)^2$

AQ = ${12}/2$ = 6

PQ = 6 - $5/2 ⇒ 7/2$ = 3.5

Answer: (a)

Let length of the side of the square = x units

∴ Length of the diagonal = $√2$ x units

ΔADE ~ ΔEFC (By AAA)

∴ ${AD}/{EF} = {DE}/{FC}$

⇒ ${q - x}/x =x/{p - x}$

⇒ $x^2 = pq–px – qx + x^2$

⇒ x = ${pq}/{p + q}$

BE = ${√2 pq}/{p + q}$ Length of the diagonal