3D Shapes

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

Which of the following is not a polyhedron?

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 $\mathrm{x}$ ?

List out five regular types of polyhedrons.

Define a polyhedron.

The icosahedron in the given images is

A polygon with $20$ sides are called

The dimensions of a cuboid are in the ratio of $1:2:3$ and its total surface area is $88 {\mathrm{m}}^2$, then the dimensions will be

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.

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:

The cost needed for painting The walls of a cuboid and celling of cuboid is $\mathrm{Rs}5000$. The perimeter of the floor is $60\mathrm{cm}$. and ratio of length and breadth of the cuboid is $3:7$. Find the height of the cuboid if the cost of painting per ${\mathrm{cm}}^2$ of cuboid is $\mathrm{Rs}5$.

A hollow cuboid of dimension approximately $30m\times 20m\times 10m$ of Capacity $800m^3$ Also its walls are $2m$ thick. Calculate the thickness of the bottom of cuboid.

Find the height of a cube whose volume is $330 {\mathrm{cm}}^3$ and base area is $15 {\mathrm{cm}}^2$.

The area of three adjacent faces of a cuboid are x,y,z, square units respectively. If the volume of the cuboid by v cube units. then the correct relation between v,x,y,z, is-