Surface Area of a Cuboid Practice Problems & Solutions

Let's go through the options:

A - In this option, we can observe that there are two flaps on the same side.

If we try to turn this net into a box, we should obtain a box where on one side there are two faces one on top of the other while the other side is "open",
meaning this net cannot be turned into a complete and full box.

B - This net looks valid at first glance, but we need to verify that it matches the box we want to draw.

In the original box, we see that we have four flaps of size 9*4, and only two flaps of size 4*4,
if we look at the net we can see that the situation is reversed, there are four flaps of size 4*4 and two flaps of size 9*4,
therefore we can conclude that this net is not suitable.

C - This net at first glance looks valid, it has flaps on both sides so it will close into a box.

Additionally, it matches our drawing - it has four flaps of size 9*4 and two flaps of size 4*4.

Therefore, we can conclude that this net is indeed the correct net.

D - In this net we can see that there are two flaps on the same side, therefore this net will not succeed in becoming a box if we try to create it.

We identified that the faces are

3*3, 3*11, 11*3
As the opposite faces of an cuboid are equal, we know that for each face we find there is another face, therefore:

3*3, 3*11, 11*3

or

(3*3, 3*11, 11*3 ) *2

To find the surface area, we will have to add up all these areas, therefore:

(3*3+3*11+11*3 )*2

And this is actually the formula for the surface area!

We calculate:

(9+33+33)*2

(75)*2

150

To solve this problem, we'll utilize the formula for the surface area of a cuboid. The steps are as follows:

• Step 1: Identify the dimensions from the problem. The dimensions provided are $a = 3$, $b = 5$, and $c = 2$.
• Step 2: Apply the surface area formula for a cuboid. The formula is: $2(ab + bc + ac)$ where $a$, $b$, and $c$ are the dimensions of the cuboid.
• Step 3: Substitute the known values into the formula: $2(3 \cdot 5 + 5 \cdot 2 + 3 \cdot 2)$
• Step 4: Calculate each term inside the parentheses: - $a \cdot b = 3 \cdot 5 = 15$ - $b \cdot c = 5 \cdot 2 = 10$ - $a \cdot c = 3 \cdot 2 = 6$
• Step 5: Sum the results from Step 4: $15 + 10 + 6 = 31$
• Step 6: Multiply the sum by 2 to find the total surface area: $2 \times 31 = 62$

Thus, after performing the necessary calculations, the surface area of the orthohedron is $62$ square units.

First, we recall the formula for the surface area of a cuboid:

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

As in the cuboid the opposite faces are equal to each other, the given data is sufficient to arrive at a solution.

We replace the data in the formula:

(8*5+3*5+8*3) *2 =

(40+15+24) *2 =

79*2 =

158

Let's see what rectangles we have:

8*5

8*12

5*12

Let's review the formula for the surface area of a rectangular prism:

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

Now let's substitute all this into the exercise:

(8*5+12*8+12*5)*2=
(40+96+60)*2=
196*2= 392

This is the solution!