3D Shapes

To which of the given solids is Euler's formula applicable?

Which of the following is not a polyhedron?

What is Euler's formula for any polyhedron? 

What is a solid made up of polygonal faces called?

A closed box is built of wood of uniform thickness. Its external dimensions are $12 \mathrm{cm}$, $10 \mathrm{cm}$ and $8 \mathrm{cm}$. If the inner surface area is $376 \mathrm{sq}.\mathrm{cm}$, then what is the thickness of the wood?

The length of a room is $\frac{21}{16}$ times its breadth and breadth is $\frac{4}{3}$ times its height. If $\mathrm{H}$ is the height of the room and $\mathrm{L}$ is the longest rod that can be placed in the room, then which one of the following is correct?

Let $\mathrm{x}, \mathrm{y}, \mathrm{z}$ be the length, breadth, height of a cuboid. If its volume is $400$ cubic $\mathrm{cm}$ and total surface area is $340$ square $\mathrm{cm}$, then what is ${\mathrm{x}}^{-1}+{\mathrm{y}}^{-1}+{\mathrm{z}}^{-1}$ equal to?

A rectangular metal sheet is of length $24 \mathrm{cm}$ and breadth $18 \mathrm{cm}$ from each of its corners a square of side $\mathrm{x} \mathrm{cm}$ is cut off and an open box is made of the remaining sheet. If the volume of the box is $640$ cubic $\mathrm{cm}$, then What is the value of $\mathrm{x}$ ?

The length of the longest pole that can be put in a room of dimensions $\left(10 m\times 10 m\times 5 m\right)$ is 

List out five regular types of polyhedrons.

Define a polyhedron.

The icosahedron in the given images is

A polygon with $20$ sides are called

How many bricks each measuring $64 \mathrm{cm}\times 11.25 \mathrm{cm}\times 6 \mathrm{cm}$, will be needed to build a wall measuring $8 \mathrm{m}\times 3 \mathrm{m}\times 22.5 \mathrm{m}$?

A room has floor size of $15\times 6 \mathrm{sq} \mathrm{cm}$. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls ?

Length of a cuboid is $40\%$ more than its breadth and its height is $30\%$ less than its breadth. If volume of the cuboid is$122500 {\mathrm{cm}}^3$ and radius of base and height of a right circular cone are $5 \mathrm{cm}$ less and 10 cm less than the height and breadth of cuboid respectively, then what is the cost of paper required to cover curved surface area of the cone if cost of paper is $\mathrm{Rs}.1.4\text{ per} {\mathrm{cm}}^2$?

A cuboid has $8$ vertices, $12$ edges and $6$ faces.

A hall is $15 \mathrm{m}$ long and $12 \mathrm{m}$ broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of hall is:

Rita and Meeta both are having lunch boxes of cuboidal shape. The length and breadth of Rita's lunch box are $10\%$ more than that of Meeta's lunch box, but the depth of Rita's lunch box is $20\%$ less than that of Meeta's lunch box. The ratio of the capacity of Rita's lunch box to that of Meeta's lunch box is:

The length, breadth and height of a cuboid are $18 \mathrm{cm}, 24 \mathrm{cm} \mathrm{and} 4 \mathrm{cm}$ respectively. The volume of cube is equal to the volume of given cuboid. The side of the cube is: