# Metal Spheres Each of Radius 2cm Are Packed into a Rectangular Box of Internal Dimension 16cm X 8cm X 8cm When 16 Spheres Are Packed the Box is Filled with Preservative Liquid. Find Volume of this Liquid? - Mathematics

Metal spheres each of radius 2cm are packed into a rectangular box of internal dimension 16cm x 8cm x 8cm when 16 spheres are packed the box is filled with preservative liquid. Find volume of this liquid?

#### Solution

Given radius of metal spheres = 2cm

Volume of sphere(v) = 4/3pir^3

So volume of each metallic sphere =4/3pi(2)^3cm^3

Total volume of 16 spheres (v_1)=16xx4/3pi(2)^3cm^3   ....(1)

Volume of rectangular box = lbh

V2 = 16 x 8 x 8cm3                 .....(2)

Subtracting (2) – (1) we get volume of liquid

⇒ V_2-V_1=Volume off liquid

⇒ 16xx8xx8-4/3pi(2)^3xx16

⇒ 1024 - 536.16 = 488cm3

∴Hence volume of liquid = 488cm3

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 44 | Page 30