Rectangular Prism Calculator

Rectangular Prism Calculator

Rectangular Prism Calculator is used to calculate the volume, Surface area, and diagonal of the prism. It also provides a step-by-step solution to every problem.

What is a Rectangular Prism?

A rectangular prism is a three-dimensional shape that has six faces and each face is a rectangle shape. Its shape is also called a rectangular cuboid or parallelepiped. The length, width, and height of the rectangular prism may be different or the same, but the angles between all faces are 90 degrees.

Formulas

The formula for the surface area of a prism is stated as.

Surface Area = 2(h x w) + 2(h x l) + 2(l x w)

The formula for the volume of a prism is stated as.

Volume = l x w x h

The formula of the diagonal of a prism is stated as.

Diagonal = √ l² + w² + h²

Where,

• l = length of the prism.
• h = height of the prism.
• w = weight of the prism.

Example

Find the volume, surface area, and diagonal of the prism if its length is 10, width is 6, and height is equal to 7.

Solution:

Step 1: Write the data from the above statement.

l = 10, w = 6, h = 7,

Volume =? 

Surface Area =? 

Diagonal =? 

Step 2: Write the formula of volume, Area, and Diagonal.

Surface Area = 2(h x w) + 2(h x l) + 2(l x w)

Cubic Volume = l x w x h

Diagonal = √ l² + w² + h²

Step 3: Put the values from “step 1” in the above formulas.

Surface Area

Surface Area = 2(h x w) + 2(h x l) + 2(l x w)

= 2(7 x 6) + 2(7 x 10) + 2(10 x 6)

= 2(42) + 2(70) + 2(60)

= 84 + 140 + 120

= 344 m²

Volume

Volume = l x w x h

= (10 x 6 x 7)

= 420 m³

Diagonal:

Diagonal = √ l² + w² + h²

= √102 + 62 + 72

= √100 + 36 + 49

= √185

= 13.601 m

More examples

Here are a few results of some other examples in the table section.