aptitude mensuration mcq pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (b)

Circumference of circular bed = 30 cm

Area of circular bed = ${(30)^2}/{4 π}$

Space for each plant = 4 $cm^2$

∴ Required number of plants

= ${(30)^2}/{4 π}$ ÷ 4 = 17.89 = 18 (Approx)

Answer: (a)

R = ${abc}/{4Δ}$

R = ${8 × 8 × c}/{4 × 1/2 × c √{64 - c^2/4}}$

5 = ${32}/{√{64 - c^2/4}}$

⇒ 64 - $c^2/4 = {1024}/{25} ⇒ c^2/4 = {576}/{25}$

⇒ $c/2 = {24}/5$ ⇒ c = 9.6 cm.

Answer: (b)

Given that, the height and radius of a right circular metal cone (solid) are 8 cm and 2 cm, respectively.

i.e., h = 8 cm and r = 2 cm

Let the radius of the sphere is R.

Then, by condition, $1/3 πr^2h = 4/3 πR^3$

⇒ 4 × 8 = 4$R^3$

⇒ $R^3 = (2)^3$

∴ R = 2

∴ Radius of the sphere = 2 cm

Answer: (c)

Volume of material in the sphere

= $[{4/3} π × ((4)^3 - (2)^3)] cm^3 = ({4/3} π × 56) cm^3$

Let the height of the cone be h cm.

Then, $1/3 π × 4 × 4 × h = (4/3 π × 56)$

= h = ${{4 × 56}/{4 × 4}}$ = 14cm

Answer: (b)

Area of the square = $(10 cm)^2 = 100 cm^2$

The largest possible circle would be as shown in the figure below :

Area of the circle = ${22}/7 × (5)^2 = {22 × 25}/7$

Required ratio = ${22 × 25}/{7 × 100} = {22}/{28} = {11}/{14}$

= 0.785 ≈ 0.8 = $4/5$