RRB RPF RPSF SI and CONS Model Papers 8 with solutions

Question : 51 of 120

Marks: +1, -0

A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm. diameter. How many such balls can be made?

Validate

Solution:

(4)

L = the radius of the cone
H = height of the cone
Volume of cone

= {1}/{3} \π {L}^{2} {H}

Let n be the no. of spherical balls then volume of the balls = volume of the cone

{n} ×{2}/{3} \π {R}^{3}=\ {1}/{3} \π {L}^{2} {h}

{n} \×4 \π {R}^{3}= {L}^{2} {H}

∴

{n}= { {L}^{2} {H}}/{4 {r}^{3}}

= {(20)^{2}× 10}/{4 × 2^{3}}

= {400 × 10}/{4 × 8}=125

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