Question

A solid has how many dimensions?

Answer 1

Hint:Every solid has 3 dimensions, because, as we call all the solids ‘3 – D’ shapes, 3 – D refers to 3 – Dimensions. In the solution, the different dimensions of different ‘3 – D’ shapes is explained.

Complete step by step answer:
The 3 dimensions of different solids are explained below:
CUBE: The formula to find the volume of cube is \[side\times side\times side\] . When we are writing\[{{(side)}^{3}}\], then we are actually multiplying three lengths with each other. When we multiply two lengths with each other then we are actually getting a figure having two dimensions. Similarly, when we multiply three lengths with each other, then we are getting a figure having three dimensions.

CUBOID:The formula used to find the volume of a cuboid if\[length\times breadth\times height\]. When we multiply them with each other, then we are actually multiplying three lengths with each other. Therefore, the figure that we are getting has 3 dimensions. If we will multiply only two lengths with each other, then the figure that we will get will have 2 dimensions.

CONE:The formula to find cone’s volume is \[\pi {{r}^{2}}h\] . In this formula also, we are multiplying the three dimensions, radius; radius; height. Therefore, this is also a 3 dimensional shape.
SPHERE:The formula to find the volume of a circle is \[\frac{4}{3}\pi {{r}^{3}}\] . In this formula also, we are writing \[radius\times radius\times radius\] , we are multiplying three lengths with each other. Therefore, the figure that we will get will be of a 3ndimensional figure.

Note:One must remember all the common and basic formulas to find the volumes of different 3 - dimensional figures as they can come in handy. Knowing all the above mentioned formulas beforehand can be very useful in difficult situations.