mensuration Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Answer: (c)

The locus of the centre of the front wheel of the bicycle is a line parallel to the path of the wheel of the bicycle at a height d/2 cm.

Answer: (a)

AM = 5 cm

BM = 3 cm

AB = 5 – 3 = 2 cm

PQ Bisect AB

∴ OA = OB = 1 cm

In ΔAOP

∴ OP = $√{AP^2 - OA^2} = √{5^2 - 1^2}$

= $√{25 - 1} ∼ = √{24} = 2 √6$

∴ PQ = 2 × OP = 2 × 2 $√6 = 4 √6$ cm

Answer: (a)

Volume of cone and pyramid = $1/3$ × Base area × Height

Since, volume of cone and pyramid are same but their surface area are not same because of their slant height.

Answer: (d)

Volume of cylinder = π $r_1^2$h

Volume of ball = $4/3πr_2^3$

Number of balls = 48

∴ Number of balls = ${\text"Volume of cylinder"}/{\text"Volume of balls"} = {πr_1^2h}/{4/3 πr_2^3}$

⇒ ${πr_1^2 h}/{4/3 πr_2^3} = 48 ⇒ {πr_1^3}/{4/3 πr_2^3}$ = 48

(∵ $r_1$ = h)

⇒ $3/4(r_1/r_2)^3 = 48 ⇒ (r_1/r_2)^3 = {48 × 4}/3$

⇒ $r_1/r_2 = (16 × 4)^{1/3} ⇒ r_2/r_1 = 1/4$

Thus, the ratio of radius of ball to cylinder is 1 : 4.

Answer: (c)

AX = $√{400 –144}$ = 16

BX = $√{256 – 144} = √{112}$ = 10.6

AB = (16 + 10.6) ≈ 26.6