Surface Area of a Cuboid Practice Problems & Solutions

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!

To solve this problem, we'll follow these steps:

• Step 1: Identify the dimensions of the cuboid.
• Step 2: Apply the surface area formula for a cuboid.
• Step 3: Calculate and interpret the result.

Now, let’s work through each step:

Step 1: We have the dimensions as follows:
- Length ($l$) = 72
- Width ($w$) = 17
- Height ($h$) = 14

Step 2: Apply the surface area formula:
The total surface area $A$ is calculated using the formula:
$A = 2(lw + lh + wh)$ Substitute the given dimensions into the formula:
$A = 2((72 \times 17) + (72 \times 14) + (17 \times 14))$

Step 3: Calculate each multiplication and sum them up:
- Calculate $72 \times 17 = 1224$
- Calculate $72 \times 14 = 1008$
- Calculate $17 \times 14 = 238$
Now substitute back into the equation:
$A = 2(1224 + 1008 + 238)$ Add the products:
$A = 2(2470)$ Finally, multiply by 2:
$A = 4940$

Therefore, the surface area of the cuboid is $4940 \, \text{square units}$.