Evaluating Volume When Side Is a Variable

Q.

Water is pouring into a cuboidal reservoir at the rate of $60$ liters per minute. If the volume of the reservoir is $108{\mathrm{m}}^3$, find the number of hours it will take to fill the reservoir.

Q. If a point $C$ lies between two points $A$ and $B$ such that $AC=BC$, then prove that $AC=\frac{1}{2}AB$. Explain by drawing the figure.

Q.

How many cubic centimetres of iron is required to construct an open box whose external dimensions are $36cm$, $25cm$ and $16.5cm$ provided the thickness of the iron is $1.5cm$. If one cubic cm of iron weighs $7.5\mathrm{g}$, find the weight of the box.

Q. The volume of the rectangular block is $\left(x\right)\left(x^2\right)\left(3x^3\right)$ cubic centimetres.
It can be simplified as.

1. $3x^6$
2. $3x^5$
3. $3x^3$

Q.

A rectangular block has its length , breadth and height as 1 m, 2m, and 3 m respectively. If all the three dimensions are increased by 1 m each , the volume of new figure will be 34 cubic metres

1. True

2. False

Q.

6 hectare = _______ sq. meter.

1. 600000 m²

2. 60000 m²

3. 6000 m²

4. 600 m²

Q.

A rectangular block has 2 metres, 3 metres and 4 metres as length, width and height respectively. If the sides of the block are extended by the same length 'x 'metres, what will be the algebric expression for the new volume?

1. $(x+2)(2x+3)(x+4)$ cubic metres

2. $(2x+2)(x+3)(x+4)$ cubic metres

3. $(x+2)(x+3)(x+4)$ cubic metres

4. $(x+2)(x+3)(2x+4)$ cubic metres

Q. Match the following to their simplified expressions.

1. $-12x^5$
2. $10x^3{y}^6$
3. $-12x^7$
4. $20x^2{y}^4$

Q. Find the cost of digging a cuboidal pit $8$ m long, $6$ m broad and $3$ m deep at the rate of $30$ per m${}^3$.

Q. If $(x-1)$ is a factor of $m{x}^2-\sqrt{2}x+1=0$, then the value of 'm ' is

1. $\sqrt{2}$
2. $\sqrt{2}+1$
3. $1$
4. $\sqrt{2}-1$

Q.

The volume of rectangular box having length, breadth and height as $(a+b),(a^2+b^2)and2a$ respectively is $2a^4+2a^2{b}^2+2a^{3}b+2a{b}^3$

1. True

2. False