Cube

Q.

The total surface area of a cone whose radius is r/2 and slant height 2l is

1. $2\mathrm{\pi r}(\mathrm{l}+\mathrm{r})$

2. $\mathrm{\pi r}(\mathrm{l}+\frac{\mathrm{r}}{4})$

3. $\mathrm{\pi r}(\mathrm{l}+\mathrm{r})$

4. $2\mathrm{\pi rl}$

Q. Find the surface area of a sphere of radius $5.6cm$

Q.

The length of the longest rod that can fit in a cubical vessel of side 10 cm, is
(a) 10 cm (b) 20 cm (c) $10\sqrt{2}$cm (d) $10\sqrt{3}$cm

Q.

A swimming pool is 18m long and 8m wide. its shallow and deep ends are 1.2m and 2m deep respectively. If the bottom of the pool slopes uniformly, then the capacity of the pool is 230.4 $m^3$

1. True

2. False

Q.

A cloth having an area of$165m^2$ is shaped into the form of a conical tent of radius $5m$ , How many students can sit in the tent if a student, on an average, occupies$\frac{5}{7}{m}^2$ on the ground?

Q. The volume of a cube of side 'a' is ____.

1. a x a x a

2. a x a

3. 3a
4. a + 3

Q.

Water is discharged from a pipe of cross section area 3.2$c{m}^2$ at a speed of 5m/s. Find the volume of water discharged in $c{m}^3$ per second.

1. 1600 $c{m}^3$

2. 1500 $c{m}^3$

3. 160 $c{m}^3$

4. 1000 $c{m}^3$

Q. Two cubes of same side 6 cm are joined end to end. Then, the total surface area of the new cuboid is

1. $546$ $c{m}^2$
2. $500$ $c{m}^2$
3. $360$ $c{m}^2$
4. $400$ $c{m}^2$

Q. If each edge of a cube is increased by $50\%$, then find the percentage increase in its surface area.

1. $125\%$
2. $150\%$
3. $175\%$
4. $110\%$

Q.

The largest cube is carved out of a sphere of diameter $10\sqrt{3}cm$. Find the volume of the cube.

1. $180c{m}^3$

Q.

A cube is a three-dimensional figure as shown in the given figure. It has six faces and all of them are identical squares. The length of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.

Q. A solid cube of edge 28 cm is melted down and recasted into smaller cubes of edge length 4 cm. Find the number of smaller cubes obtained.

1. 343
2. 356
3. 396
4. 368

Q.

What is the difference between the number of edges and number of faces of a cube?

1. 0

2. 4

3. 2

4. 6

Q. Each edge of a cube is increased by $50\%$, then percentage increase in its surface area =.

1. $150\%$
2. $110\%$
3. $125\%$

Q.

The surface area of a cuboid with dimensions 12 cm × 15 cm × 9 cm is

1. 826 cm²

2. 816 cm²

3. 836 cm²

4. 846 cm²

Q. Question 66 (i)

How many edges does the following solid have?

Cone

Q. Question 65 (ii)

How many vertices does the following solid have?

Cylinder

Q. 12. If l is the length of diagonal of cube volume V then a 3V=l B 3V = l C 33V = 2l D 33 = l

Q. If each edge of a cube is increased by $50\%$, then find the percentage increase in its surface area.

1. $125\%$
2. $150\%$
3. $175\%$
4. $110\%$

Q. A match box measures $4\text{cm}\times 2.5\text{cm}\times 1.5\text{cm}.$ Find the volume of a packet containing 12 such boxes (no space is left in the packet)..........[3 marks]

Q. Question 5
Is a square prism same as a cube? Explain.

Q. How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?

1. 36
2. 232
3. 216
4. 484

Q.

The largest cube is carved out of a sphere of diameter $10\sqrt{3}cm$. Find the volume of the cube.

1. $180c{m}^3$

2. $1000c{m}^3$

3. $100\sqrt{3}c{m}^3$

4. $80c{m}^3$

Q. If each edge of a cube is increased by $50\%$, the percentage increase in its surface area is:

Q. Each edge of a cube is increased by $50\%$, then percentage increase in its surface area =.

1. $110\%$
2. $150\%$
3. $125\%$

Q. A cube has ____ edges.

1. 4
2. 8
3. 12
4. 6

Q. If each edge of a cube is increased by $50\%$, then its total surface area is increased by .

1. $110\%$
2. $150\%$
3. $125\%$
4. $175\%$

Q. Each edge of a cube is increased by $50\%$, then percentage increase in its surface area =.

1. $125\%$
2. $110\%$
3. $150\%$

Q.

Which of the following statements are true?

(i) All cubes are cuboids.

(ii) All cuboids are cubes.

(iii) A cube has 6 faces, 8 corners, and 12 edges.

(iv) A cube has 8 faces, 12 corners, and 6 edges.

1. (i)

2. (i) and (iii)

3. (ii) and (iv)

4. (i) and (iv)

Q. If each edge of a cube is increased by $50\%$, then its total surface area is increased by .

1. $125\%$
2. $150\%$
3. $175\%$
4. $110\%$