A rectangular container, whose base is a square of side 5 cm, sta… - Vidyadip

Question

A rectangular container, whose base is a square of side $5\ cm,$ stands on a horizontal table, and holds water up to $1\ cm$ from the top. When a solid cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic $cm$ of water overflows. Calculate the volume of the cube and also the length of its edge.

✓

Answer

Let the length of each edge of the cube be $'x\ ’ \ cm$
Then, volume of the cube $=$ Volume of water inside the tank $+$ Volume of water that overflowed
$x^3 = (5 \times 5 \times 1) + 2$
$x^3 = 27$
$x = 3\ cm$
Hence, volume of the cube $= 27\ cm^3$
And edge of the cube $= 3\ cm$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Surface Area And Volume of A Cuboid And Cube→Surface Area And Volume of A Cuboid And Cube — all question types→MATHS STD 9 question papers→Rajasthan Board STD 9 question papers→Rajasthan Board question paper generator→

Similar questions

Find the volume and surface area of a sphere whose radius is: $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
5m

In figure, ABC is a right angled triangle at A, BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment $\text{AX}\perp\text{DE}$ meets BC at Y. Show that:

$\text{ar}(\text{CYXE})=\text{ar}(\text{ACFG})$

If the median of scores $\frac{\text{x}}2{},\frac{\text{x}}3{},\frac{\text{x}}4{},\frac{\text{x}}5{}$ and $\frac{\text{x}}6{}$ (where x > 0) is 6, then find the value of $\frac{\text{x}}6{}.$

Prove that:
$9^{\frac{3}{2}}-3\times5^0-\Big(\frac{1}{81}\Big)^{\frac{-1}{2}}=15$

Factorize the following expressions : $\Big(\text{a}^3-\frac{1}{\text{a}^3}\Big)-2\text{a}+\frac{2}{\text{a}}$

In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division: $f(x) = 4x^3 - 12x^2 + 14x - 3, g(x) = 2x - 1$

A cube of side $4\ cm$ contains a sphere touching its side. Find the volume of the gap in between.

If O is the centre of the circle, find the value of x in the following figures:

Angles opposite to equal sides of an isosceles triangle are equal.This result can be proved in many ways. One of the proofs is given here.

Find the value $k$ if $x - 3$ is a factor of $k^2x^3 - kx^2 + 3kx - k.$