Metal spheres each of radius 2 cm are packed into a rectangular box of internal dimensions 16 cm X 8 cmX into 8 cm and 16 squares are packed the box is filled with preservative liquid find the volume of this liquid give your answer to nearest integer
Answers
Answer:
The volume of the liquid is 488 cm³.
Step-by-step explanation:
Given :
Radius of the metallic sphere, r = 2 cm
Dimension of rectangular box = 16 × 8 × 8
Volume of the sphere = 4/3πr³
Volume of 16 spheres = 16 × 4/3πr³
Volume of the 16 spheres = 64/3π(2)³ ……..(1)
Volume of the rectangular box= lbh = 16 × 8 × 8 cm³………………(2)
Volume of the liquid = Volume of a rectangular box - Volume of 16 spheres
= 16 × 8 × 8 - 64/3π(2)³
[From eq 1 & 2]
= 1024 - 64/3 × 22/7 × 8
= 1024 - 11264/21
= 1024 – 536.38cm³
= 487.62 cm³ ≈ 488 cm³
Volume of the liquid = 488 cm³
Hence,The volume of the liquid is 488 cm³
HOPE THIS ANSWER WILL HELP YOU….
π = 3.14
Volume of the metal box = 16*8*8 = 1024 cm^3
Volume of 16 metal spheres = 16*4/3*3.14*2*2*2
= 512*3.14/3
=535.89cm^3
Volume of the liquid = Volume of metal box - Volume of metal spheres
= 1024cm^3 - 535.89cm^3
= 488.11cm^3
= 488cm^3 ( to the nearest integer)