Calculate Cuboid Surface Area: Given Volume 72 cm³ and Length 6 cm

Question

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

Solution Steps

00:00 Calculate the surface area of the box
00:03 Let's use the formula for calculating box volume
00:10 height times length times volume
00:14 Let's mark the box length as X
00:25 We'll substitute appropriate values and solve for X
00:43 This is the box length
00:51 Let's use the formula for calculating surface area
00:56 2 times (sum of face areas)
01:11 We'll substitute appropriate values and solve for surface area
01:27 Let's solve each multiplication separately
01:44 And this is the solution to the problem

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