Question

A glass cylinder with diameter 28 cm has water to a height of 10 cm. A metal cube of 9 cm edge is immersed in it completely. Calculate the height (up to 2 decimal place) by which water will rise in the cylinder. [Use pi=22/7] ​

Answer 1

Answer:

Suppose the water rises by h cm.

Volume of water displaced = Volume of the cube of edge 8 cm

πr

2

h=8

3

3.14×10

2

×h=8×8×8

h=1.6 cm

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

• A glass cylinder with diameter 28 cm has water to a height of 10 cm.

• A metal cube of 9 cm edge is immersed in it completely.

Let assume that height by which water level rises in the cylinder be h cm.

Now, we have

• Radius of cylinder, r = 14 cm

• Height of cylinder = h cm

• Edge of cube, a = 9 cm

We know, Amount of water displaced in the glass cylinder is equals to volume of cube.

So,

$\rm \: Volume_{(water displaced)} \: = \: Volume_{(Cube)}$

$\rm \: \pi {r}^{2}h \: = \: {a}^{3}$

$\rm \: \dfrac{22}{7} \times 14 \times 14 \times h \: = \: 9 \times 9 \times 9$

$\rm \: 22 \times 2\times 14 \times h \: = \: 9 \times 9 \times 9$

$\rm \: h \: = \: \dfrac{9 \times 9 \times 9}{44 \times 14}$

$\rm\implies \:h \: = \: 1.18 \: m \:$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$