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

Answer: (a)

∠A = 360° – Ext ∠A. ....(i)

∠B = 360 – Ext ∠B .... (ii)

∠C = 360 – Ext ∠C .... (iii)

A B C .

Similarly,

∠A + ∠B + ∠C =180°

From Eqs. (i), (ii), (iii) and (iv),

360° – Ext ∠A +360° – Ext ∠B + 360° – Ext ∠C = 180°

⇒ Ext ∠A +Ext ∠B +Ext ∠C

= 1080° – 180°

= 900°

Answer: (a)

Volume of bigger cone

= $1/3 π(6)^2 × 8 = 96 π cm^3$

Volume of smaller cone = $1/3 π (1)^2 × 2$

= ${2π}/3 cm^3$

Number of cones = ${96 π}/{{2π}/3}$ = 144

Answer: (c)

We know that, the sum of two sides is always greater than third side.

∴ 10 + 100 > x ...(i)

x > 100 – 10 and x > 90 ...(ii)

Difference of two sides of a triangle is always less than third side.

From Eqs. (i) and (ii),

we get,

90 < x < 110

Answer: (b)

Increase in the height of water level

= ${0.75}/{2.5 × 1.5}$m = 0.2 m = 20 cm

Answer: (c)

Volume of solid metallic cylinder = π $r^2$h

= π × 36 × 10 = 360 π

flat surface area of cylinder = 2π $r^2$

= 2 × π × 6 × 6 = 72π

After melted to make two cones in the ratio of volume 1 : 2

volume of first cone = $1/3 π r_1^2h$ = 120π

$r_1^2$h = 360

∴ $r_1^2$ = 36

volume of second cone = $1/3 π r_2^2h$ = 240 π

$r_2^2h$ = 720

∴ $r_2^2$ = 72

Flat surface area of two cone = 72p + 36p = 108p

Change in surface = 108π – 72π = 36π

% change = ${36 π}/{72 π}$ × 100 = 50%