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

Answer: (c)

Let l be the length and b be the breadth of cold storage.

L = 2B, H = 3 metres

Area of four walls = 2[L × H + B × H] = 108

⇒6BH = 108⇒B = 6

∴ L = 12, B = 6, H = 3

Volume = 12 × 6 × 3 = 216 $m^3$

Answer: (b)

Total surface area of a cube = $6a^2$

⇒ 6 = $6a^2 ⇒ a^2$ = 1

∴ a = 1 unit

Volume of the cube = $a^3 = 1^3$ = 1 cu unit

Answer: (c)

Let the cone is divided into two parts by a line l.

Now triangle ACD and AOB are similar.

(According to proportionality theorem)

CD = $r/2, since AC = h/2$

Required ratio = ${\text"Volume of original cone"}/{\text"Volume of smaller cone"}$

= ${1/3 π r^2 h}/{1/3 π (r/2)^2 (h/2)} - 8/1$

∴ Required ratio = 8 : 1

Answer: (a)

We have BE || AC (Given)

So ∠ADE = ∠B and ∠AED = ∠C

(corresponding angles)

Therefore ΔABC ∼ ΔADE by A similarity criterion. Also given area of ΔABC = 2 area of ΔADE ...(1) We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

⇒ ${ar (ABC)}/{ar (ADE)} = ({AB}/{AD})^2$ ...(2)

From (1) we get

${ar(ABC)}/{ar(ADE)} = 2/1$ ...(3)

Therefore from (2) and (3)

$({AB}/{AD})^2 = 2/1$

⇒ ${AB}/{AD} = √2/1$

⇒ $1/{AD} = √2 unit (∵ AB = 1 unit)$

AD = $1/√2$ units

∴ Option (a) is correct.

Answer: (d)

In any triangle, sum of two sides is always greater than third side.

I. AC – AB < BC ⇒ AC < BC + AB {True}

II. BC – AC < AB ⇒ BC < AB + AC {True}

III. AB – BC < AC ⇒ AB < AC + BC {True}