Question

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer, [use π = 3.14] A. 493 cm3 B. 488 cm3 C. 427 cm3 D. 431

explain. it​

Answer 1

Metal spheres each of radius 2 cm are packed into a rectangular box of dimensions 16 cm ×8cm×8cm when 16 spheres are packed in the box it is filled with preservative liquid find the volume of this liquid to the nearst integer

Answer 2

Answer:

$488.16 {cm}^{3}$

Step-by-step explanation:

${\pink {\bold{ \underline{given \: }}}}$

$\star \bold{radius \: of \: sphere = 2cm}$

$\star \bold{rectangular \: sphere \: dimension = 16cm \times 8cm \times 8cm}$

$\star \bold{box \: is \: filled \: with \: 16 \: spheres \: .}$

${\pink{ \bold{ \underline{to \: find : }}}}$

$\star \bold{volume \: of \: liquid}$

${\pink{ \bold{ \underline{list \: of \: formulas \: \: used}}}}$

$\bf \: \implies volume \: of \: cube \: = l \times b \times h$

$\bf \implies \: volume \: of \: sphere \: = \frac{4}{3} {\pi}r^{3}$

$\bf \implies \: volume \: of \: liquid \: will \: be : \\ \\ \bf \: volume \: of \: box \: - volume \: of \: sphere \:$

${\pink {\bold{ \underline{solution : }}}}$

${\small \sf{volume \: of \: cube \: = l \times b \times h}}$

$\sf{ \implies \: 16 cm \times 8cm \times 8cm} \\ \\ \implies \sf{1024 {cm}^{3} }$

$\sf {volume \: of \: sphere = \frac{4}{3} \pi \: {r}^{3} }$

$\implies \sf{volume \: of \: 16 \: sphere \: = 16 \times \frac{4}{3} \times 3.14 \times 8 }$

$\sf \implies \: volume \: of \: 16 \: sphere = 535.84 {cm}^{3}$

$\sf \: volume \: of \: liquid = volume \: of \: box \: - \: volume \: of \: sphere$

$\sf \implies 1024 {cm}^{3} - 535.84 {cm}^{3} \\ \implies \: 488.16 {cm}^{3}$