Name: How Are 3d Solids Different From 2d Shapes?
Uploaded: 2019-07-19
Duration: 5 min 38 s
Description: Do you know that a 2D shape has two dimensions: length and breadth, and a 3D shape has three dimensions: length, breadth, and height? Let us learn about 3D shapes in detail.

Question

In each prism here the base shapes is highlighted.

Focusing on triangular and rectangular prisms, create a table like this one and determine the specific formula to calculate the volume of rectangular and triangular prisms.

$3 D$ shape	Name of base shape	Area formula of base shape	General volume formula	Specific volume formula of the prism
Rectangular prism			Volume $=$ Area of base $\times$ Height
Triangular prism			Volume $=$ Area of base $\times$ Height

Accepted Answer

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle is the base of a three dimensional object.

A prism is a shape with two identical shapes facing each other. These identical shapes are called base.

Here, we have

The base of the above prism is triangle.

Area of triangle $= \frac{1}{2} \times base \times height$

So, the specific volume formula of the prism $= \frac{1}{2} \times b \times h \times l$

Similarly, consider the following rectangular prism,

The base of the above prism is rectangle.

Area of rectangle $= Length \times Breadth$

So, the specific volume formula of the prism $= l \times b \times h$

So, the complete table is,

$3 D$ shape Name of base shape Area formula of base shape General volume formula Specific volume formula of the prism

Rectangular prism Rectangle $Length \times Breadth$ Volume $=$ Area of base $\times$ Height $l b h$

Triangular prism Triangle $\frac{1}{2} \times base \times height$ Volume $=$ Area of base $\times$ Height $\frac{1}{2} l b h$

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