Solids with a Pair or More of Identical Faces

Q. If the total surface area of a cube is 486 $c{m}^2$, find the volume of the cube.

1. 343 $c{m}^3$
   
2. 481 $c{m}^3$
   
3. 729 $c{m}^3$
   
4. 981 $c{m}^3$
   

Q.

There are 2 cubes A and B each of volume X $c{m}^3$. Cube B is cut into smaller cubes each of volume Y $c{m}^3$. The surface area and volumes of the resulting cubes are compared.

S1: The ratio of volumes of A and B = 1:1

S2 : The ratio of surface areas of A and B = 1:1

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

Q. Every cube is a cuboid. State with true or false.

1. False
2. True

Q.

A cuboid whose length, breadth and height are equal is called a ___.

1. Cube

2. Cuboid

3. Hexagon

4. Pentagon

Q.

A 3×3×3 rubik's cube has a volume of 27 $c{m}^3$. Find the volume of each indvidual small cube.

Q. The volume of a cube is $64c{m}^3.$ Its surface area is:

Q.

Question 97

How many cubes each of side 0.5 cm are required to build a cube of volume of $8c{m}^3$?

Q.

There is a cuboidal warehouse of length, breadth and height 20 cm, 12 cm, and 8 cm respectively.

Find the number of cubical boxes of size 4 cm that can fit in the warehouse?

1. 30

2. 50

3. 40

4. 20

Q.

Total surface area of a cube is directly proportional to ___ of each side of the cube.

Q. A barn with a flat roof is rectangular in shape, $10m$. wide, $13m$. long and $5m$. high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total area in sq. m. to be painted is:

1. 460
   
2. 360
   
3. 590
   
4. 490
   

Q.

Two rectangular boxes have the same height and length, but different widths as shown in the figure.

The difference in their volumes is 360 cm³. Find their height.

1. 18 cm

2. 15 cm

3. 16 cm

4. 14 cm

Q. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?

1. 6 litres
2. 0.006 litres
3. 6000 litres
4. 60 litres

Q.

A cuboid whose length, breadth and height are equal is called a ___________.

1. Hexagon

2. Pentagon

3. Cube

4. Cuboid

Q.

The side of a cube is 6 cm. The ratio of its surface area and volume is ___ .

Q.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25cm. Find how much he would spend for the tiles, if the cost of the tiles is ₹360 per dozen.

Q. $\text{If the volume of a cube is}{a}^3,$
$\text{then its sides will be}a.$

1. True
2. False

Q. $\text{If the volume of a cube is}{a}^3,$
$\text{then its sides will be}a.$

1. True
2. False

Q. The perimeter of a triangle with sides 7 cm, 8 cm, 9 cm is ___ .

1. 21 cm
2. 22 cm
3. 23 cm
4. 24 cm

Q.

A cuboid whose length, breadth and height are equal is called a ___________.

1. Hexagon

2. Pentagon

3. Cube

4. Cuboid

Q. What is the area of a rhombus with diagonals 7 cm and 12 cm?

1. 84 sq. cm
2. 21 sq. cm
3. 42 sq. cm
4. 32 sq. cm

Q. What is the perimeter of a rectangle with dimensions 6 cm x 10 cm?

1. 30 cm
2. 32 cm
3. 34 cm
4. 36 cm

Q.

There are 2 cubes A and B each of volume X $c{m}^3$. Cube B is cut into smaller cubes each of volume Y $c{m}^3$. The surface area and volumes of the resulting cubes are compared.

S1: The ratio of volumes of A and B = 1:1

S2 : The ratio of surface areas of A and B = 1:1

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

Q. The top view of

1. True
2. False

Q. Fill in the blanks to make the following statements true:

Q. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?

1. 60 litres
2. 6000 litres
3. 6 litres
4. 0.006 litres

Q. $\text{If the volume of a cube is}{a}^3,$
$\text{then its sides will be}a.$

1. True
2. False

Q. Perimeter of a square with side length l units is ___ .

1. 4l units
2. l units
3. 2l units
4. 3l units