Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.(Use π=669/213)
Answers
The volume of this liquid is - 487.962cm³
(Use π=669/213)
Volume of Rectangular box = 16×8×8cm³ = 1024cm³
Radius of sphere, 'r' = 2cm
Volume of 1 sphere = 4/3πr³ = 4/3×π×8cm³ = 32/3πcm³
Volume of 16 spheres = 16 × 32/3 × 669/213
Volume = 536.038cm³
Volume of rest of the space = 1024-536.038cm³ = 487.962cm³
Answer:-
★ATQ:-
Radius of each sphere, r = 2 cm
Volume of a sphere is given by
Volume of 1 sphere = 4/3 πr³
Since there are 16 spheres in our question,
Volume of 16 spheres = 16 × 4/3 πr³
= 16 × 4/3 × 3.14 × 2³
= 535.89 cm³
★ We know that,
Dimensions of rectangular box = 16 cm × 8 cm × 8 cm
Volume of rectangular box = 16 × 8 × 8 = 1024 cm³
In order to find volume of the liquid that is filled in rectangular box,
★ So,
Volume of the liquid = (Volume of the rectangular box) – (Volume of the 16 spheres)
→ Volume of the liquid = 1024 – 535.89
= 488.11 cm³
Thus, volume of this liquid is 488.11 cm³.