Volume of a Cube

Q. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate is

1. 122444
2. 144244
3. 142442
4. 142244

Q.

Find the ratio of the volume of a cube to that of a sphere which will fit inside it.

Q.

Water is flowing at a rate of $7\mathrm{m}/\mathrm{s}$ through a circular pipe whose internal diameter is $2\mathrm{cm}$ into a cylindrical tank the radius of whose base is $40\mathrm{cm}$. Determine the increase in water level in $\frac{1}{2}\mathrm{hours}$?

Q.

Question 8
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate is

Thinking process- If we divide the total volume filled by marbles in a cube by volume of a marble, then we get the required number of marbles.

(A) 142296
(B) 142396
(C) 142496
(D) 142596

Q.

Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 12$\sqrt{3}$ cm. Find the edges of the three cubes.

Q.

The volumes of two cubes are in the ratio $8:27$. Find the ratio of their surface areas.

Q. The dimensions of a metallic cuboid are $100\mathrm{cm}\times 80\mathrm{cm}\times 64\mathrm{cm}$. It is melted and recast into a cube. Find the surface area of the cube.
[CBSE 2011]

Q. If the radius of a sphere is 12 cm, then find its total surface area . (Take $\pi =3.14)$

1. $2808.64c{m}^2$
2. $1800.64c{m}^2$
3. $1900c{m}^2$
4. $1808.64c{m}^2$

Q.

The dimensions of a cuboid are in the ratio of 1: 2: 3 and its total surface area is 88 $m^2$. Find the dimensions and volume of the cuboid.

Q.

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

Q.

A glass cylinder with diameter $20cm$ has water to a height of $9cm$. A metal cube of $8cm$ edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.

Q. A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm $\times$ 16 cm $\times$ 10 cm . If the mortar occupies $\frac{1}{10}th$ of the volume of the wall, then find the number of bricks used in constructing the wall.

Q.

Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.

Q. How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm $\times$ 11 cm $\times$ 12 cm?

Q.

The total surface area of a cube is $216{\mathrm{cm}}^2$ then its volume is

1. $216$

2. $144$

3. $196$

4. $212$

Q. A plate of metal 1cm thick, 9cm broad and 81cm is melted into a cube. find the difference in the surface area of the two solid.

Q.

If each edge of a cube is doubled, how many times will its volume increase?

Q. If the sphere has a surface area of 256π cm${}^2$, what is its volume (approximated value)?

1. $583\pi c{m}^3$
2. $883\pi c{m}^3$
3. $483\pi c{m}^3$
4. $683\pi c{m}^3$

Q.

Based on the statements given below, choose the correct option.
S1 : Total surface area of a cuboid is the sum of areas of four of its faces, leaving the top and bottom faces.
S2 : Lateral surface area of a cuboid is the sum of areas of four of its faces, leaving the top and bottom faces.
S3 : Area of a face of a cuboid is of the form $xy,$ where $x$ and $y$ are the length and breadth of that face respectively.

1. S1 and S3 are false

2. S2 and S3 are true

3. S1 , S3 are true

4. S2 , S3 are false

Q.

The volume of a cube is 2744 $c{m}^3$. Its surface area is

(a) 196 $c{m}^2$ (b) 1176 $c{m}^2$ (c) 784 $c{m}^2$ (d) 588 $c{m}^2$

Q.

A solid metallic cuboid of dimensions $9m\times 8m\times 2$ m is melted and recast into solid cubes of edge 2m. Find the number of cubes so formed.

Q.

A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of $97$ bricks. Each row must be decreased by $2$ bricks on each end and the construction should stop at $25th$ row. How many bricks does he need to buy?

Q. How many cubes of edge 7 cm can be cut out from a cuboid of dimension 21cm*35cm*55cm.

Q.

If one side of a cube is $15\mathrm{m}$ in length, find its volume.

Q.

An open box is made from a square lamina of side 12cm, by cutting equal squares at the corners and folding up the remaining flaps. The volume of this box cannot be

1. 115 c.c.

2. 120 c.c.

3. 125 c.c.

4. 130 c.c.

Q.

The length , width and height of a wall are 50m , 80cm and 4.5m respectively. 1/9th of its volume is mortar. Find the number of bricks in it if the dimension of each brick is 25cm * 10cm * 4cm.

Q.

The total surface area of a cube is 864 $c{m}^2.$ Its volume is

(a) 3456 $c{m}^3$ (b) 432 $c{m}^3$ (c) 1728 $c{m}^3$ (d) 3456 $c{m}^3$

Q.

The area of one face of a cube is $100m^2$. Find the volume of the cube.

1. 3000 $m^3$

2. 2000 $m^3$

3. 1000 $m^3$

4. 500 $m^3$

Q. 36. What is the volume of a cube whose surface area is 150m 2

Q. If the edge of a cube increases by $10$%, then find the percentage increase in its volume.

1. $20$%
2. $30$%
3. $66.6$%
4. $33.1$%