How many small solid spheres each of 5 mm radius can be made out of a metallic solid cone whose base...........

Quantitative Aptitude (CGL) Mensuration 3D

How many small solid spheres each of 5 mm radius can be made out of a metallic solid cone whose base has radius 21 cm and

height 30 cm?

This questions was previously asked in

SSC CGL 12th April 2022 Shift-3

32000

26460

25000

18260

Let’s solve the problem step by step:

- Volume of the cone:

Formula: V = (1/3)pr²h

r = 21 cm, h = 30 cm

V_cone = (1/3) × p × (21)² × 30 = (1/3) × p × 441 × 30 = (1/3) × p × 13230 = 4410p cm³

- Volume of one small solid sphere:

Radius = 5 mm = 0.5 cm

V_sphere = (4/3)pr³ = (4/3)p × (0.5)³ = (4/3)p × 0.125 = (1/6)p cm³

- Number of spheres = Volume of cone ÷ Volume of one sphere

Number = 4410p ÷ (1/6)p = 4410 × 6 = 26460

Now, checking the options:

- Option 1: 32000

- Option 2: 26460

- Option 3: 25000

- Option 4: 18260

Correct Answer:

Option 2 – 26460 is correct.

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