Cube

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

1. (i) and (iii)

2. (ii) and (iv)

3. (i) and (iv)

4. only (i)

Q. If a sheet measuring 1 m² costs ₹ 20, then the cost of the sheet required for making a cubical stand of edge 2.5 m, which is open from the top, is _______ .

1. ₹ 600
2. ₹ 625
3. ₹ 655
4. ₹ 675

Q. Each face of a cube is a

1. triangle
2. square
3. rectangle
4. rhombus

Q.

A cube of edge ‘k’ is divided into ‘n’ equal cubes. Determine the edge of the new cube.

1. $\sqrt{nk}$

2. $\sqrt[3]{3n}$

3. $\frac{k}{\sqrt[3]{3n}}$

4. $\frac{\sqrt[3]{3n}}{k}$

Q. The number of cubes of side 3 cm that can be cut from a cube of side 6 cm is

1. 6 cm
2. 5 cm
3. 7 cm
4. 8 cm

Q. Three cubes with sides in the ratio $3:4:5$ are melted to form a single cube whose diagonal is $12\sqrt{3}cm$. Identify the sides of the cubes

1. $3cm,4cm,5cm$
2. $9cm,12cm,15cm$
3. $6cm,8cm,10cm$
4. None of these

Q. Each edge of a cube is increased by $50$%. Find the percentage increase in the surface area of the cube.

Q. If the side of a cube is tripled, by what factor does its lateral surface area change?

1. 9

Q. The square of the length of a rod $AB$ is $72{cm}^2$. If we place the rod in the corner of a room, so that the end $A$ is always on the edge between the two walls of the corner and the end $B$ is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?

1. $6$ ${cm}^2$
2. $24$ ${cm}^2$
3. $12$ ${cm}^2$
4. $18$ ${cm}^2$

Q.

A cube of edge $k$ is divided into $n$ equal cubes. Determine the edge of the new cube

1. $\sqrt{nk}$

2. $\frac{\mathrm{k}}{\sqrt[3]{\mathrm{n}}}$

3. $\sqrt[3]{\mathrm{nk}}$

4. $\frac{\sqrt[3]{\mathrm{n}}}{\mathrm{k}}$