Examples with solutions for Surface Area of a Cuboid: Finding Area based off Perimeter and Vice Versa

Exercise #1

Given that the volume of the cuboid is equal to 72 cm³

The length of the cuboid is equal to 6 cm and the height is equal to half the length.

Calculate the surface of the cuboid

666

Video Solution

Step-by-Step Solution

The first step is to calculate the relevant data for all the components of the box.

The length of the box = 6

Given that the height of a cuboid is equal to half its length we are able to deduce the height of the box as follows : 6/2= 3

Hence the height = 3

In order to determine the width, we insert the known data into the formula for the volume of the box:

height*length*width = volume of the cuboid.

3*6*width = 72

18*width=72

We divide by 18:

Hence the width = 4

We are now able to return to the initial question regarding the surface of the cuboid.

Remember that the formula for the surface area is:

(height*length+height*width+length*width)*2

 

We insert the known data leaving us with the following result:

(3*6+4*3+4*6)*2=

(12+24+18)*2=

(54)*2=

108

Answer

108 cm²

Exercise #2

The volume of a rectangular cuboid 320 cm³.

The area of the rectangular face 80 cm².

Work out the surface area of the cuboid.

Video Solution

Answer

352cm2 352\operatorname{cm}^2

Exercise #3

The surface area of the cuboid in the diagram is 450x cm².

a = 7

Calculate the volume of the cuboid.

aa

Video Solution

Answer

225x49 225x -49 cm³

Exercise #4

The surface area of a rectangular prism 240 cm².

What is its volume according to the dimensions given in the diagram?

123

Video Solution

Answer

201.6cm3 201.6cm^3