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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 12.4 in Chapter 12 - Surface Areas and Volumes

Question 20 Surface Areas and Volumes - Exercise 12.4

16 glass sphere each of radius 2 cm are packed into cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.

Answer:

16 spheres in cuboidal box.

l = 16 cm

b = 8 cm

h = 8 cm

Volume of water filled in the box = Volume of box – Volume of 16 glass spheres

∴ Vol. of water filled in the box = lbh-16\ \times\frac{4}{3}\pi r^3

=16\times8\times8\ −\ 16\times\frac{4}{3}\times\frac{22}{7}\times2\times2\times2

=16\times8\times8-16\times8\times\frac{4}{3}\times\frac{22}{7}

=16\times8\left(8-\frac{88}{21}\right)

=16\times8\left(\frac{168-88}{21}\right)

=\frac{16\times8\times80}{21}

=\frac{10240}{21}cm^3

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