mensuration area volumes Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (a)

Let ABC be an equilateral triangle and x, y, z are points on BC, CA and AB.

Also given

BX = CY = AZ

Since ∠A = ∠B = ∠C = 60° (Equilateral triangle)

⇒ If BX = CY

⇒ ∠X = ∠Y

BX = AZ

⇒ ∠X = ∠Z

Also If ∠Y = Az

⇒ ∠Y = ∠Z

⇒ ∠X = ∠Y = ∠Z = 60°

Δ XYZ is an equilateral triangle.

Consider triangle Δ ABC and ΔXYZ

Since ∠X = ∠Y = ∠Z = 60°

and ∠A = ∠B = ∠C = 60°

⇒ ΔABC ∼ ΔXYZ ∼ by AA similarity criterion

∴ Option (a) is correct.

Answer: (a)

Given that AB = 4 cm and CD = 10 cm, let the radius of the circle be r cm.

Since the perpendicular from the center of a circle to a chord bisects the chord, therefore AO = OB = 2 cm and CP = PD = 5 cm.

In ΔAOX, by Pythagoras theorem, we have

$2^2 + (3 + x)^2 = r^2 ⇒ 4 + 9 + 6x + x^2 = r^2$ ...(1)

Similarly, in ΔCPX, we have

$5^2 + x^2 = r^2 ⇒ 25 + x^2 = r^2$ ...(2)

Equation (1) and (2) gives

$4 + 9 + 6x + x^2 = 25 + x^2 ⇒ 13 + 6x = 25 ⇒ 6x$

= 12 ⇒ x = 2

Now, equation (2) gives

25 + 4 = $r^2 ⇒ r^2 = 29 ⇒ r = √{29}$ cm

Answer: (a)

Hence, the locus of a point is the circumference of the circle with AB as diameter.

Answer: (a)

Volume of a spherical shell

= $4/3 π(R^3 - r^3)$

= $4/3 π(5^3 - 4^3)$

= $4/3$ π × 61

= ${244π}/3$

Answer: (c)

Since interior angle of the regular polygon = 140°

Hence exterior angle = 180° – 140° = 40°

∴ No. of sides = ${360°}/{\text"Exterior angle"} = {360}/{40}$ = 9

∴ No. of vertices or sides = 9

∴ Option (b) is correct.