3D Solids as an Extension of 2D Figures

Q.

The areas of three adjacent faces of a cuboid are $x,y$ and $z.$ If the volume is $V,$ then $V^2$ is equal to :

1. $\frac{x^2{y}^2}{z^2}$

2. $\frac{xy}{z}$

3. $\frac{yz}{x^2}$

4. $xyz$

Q. Find
(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is $4.2m$ in diameter and $4.5m$ high.
(ii) How much steel was actually used, if $\frac{1}{12}$ of the steel actually used was wasted in making the tank?

Q.

A small indoor greenhouse is made entirely of glass panes held together with tape. It is $30cm$ long, $25cm$ wide and $25cm$ high. How much of tape is needed for all the 12 edges?

1. $230cm$

2. $320cm$

3. $302cm$

4. $203cm$

Q. If we sharpen a pencil at one edge, it is a combination of:

1. cylinder and cone
2. frustum and a cylinder
3. frustum and cuboid
4. cylinder and hemisphere

Q. The diagonals of the three faces of a cuboid are $x,y,z$ respectively. What is the volume of the cuboid?

1. $\frac{xyz}{2\sqrt{2}}$
2. None of the above
3. $\frac{\sqrt{(y^2+z^2)(z^2+x^2)(x^2+y^2)}}{2\sqrt{2}}$
4. $\frac{\sqrt{(y^2+z^2-x^2)(z^2+x^2-y^2)(x^2+y^2-z^2)}}{2\sqrt{2}}$

Q.

There is a thin metal plate of length and breadth $2Mmm$ and $2Kmm$ respectively. Its thickness is $1mm.$ If $‘N^{\prime }$ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

1. None of these

2. Cuboid, $MKN$

3. Cuboid, $4MKN$

4. Cube, $4MKN$

Q. Stacking _____ on top of each other forms a cylinder.

1. triangles
2. circles
3. rectangles
4. squares

Q.

The cross section of a cylinder is

1. 703.36 Cubic Centimeters

2. 603.26 Cubic Centimeters

3. 735 Cubic Centimeters

4. 782 Cubic Centimeters

Q. A wall $15m$ long, $30cm$ wide and $4m$ high is made of bricks, each measuring $(22cm\times 12.5cm\times 7.5cm)$. If $1/12$ of the total volume of the wall consist of mortar, how many bricks are there in the wall?

Q. The areas of three adjacent faces of a cuboid are x, y and z then the volume of the cuboid is

1. xy
2. xyz
3. $\sqrt{xyz}$
4. $\sqrt[3]{3xyz}$

Q.

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that $V^2=xyz.$

Q.

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 9 cm × 9 cm × 6 cm, is:

1. 26
2. 9
3. 10
4. 18