Surface Area of a Cuboid - Examples, Exercises and Solutions

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!
 

Remember that the formula for the surface area of a cuboid is:

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

We input the known data into the formula:

2*(3*2+2*5+3*5)

2*(6+10+15)

2*31 = 62

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

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 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 $4940 \, \text{square units}$.

Every cuboid is made up of rectangles. These rectangles are the faces of the cuboid.

As we know that in a rectangle the parallel faces are equal to each other, we can conclude that for each face found there will be two rectangles.

Let's first look at the face painted orange,

It has width and height, 5 and 3, so we already know that they are two rectangles of size 5x6

Now let's look at the side faces, they also have a height of 3, but their width is 6,

And then we understand that there are two more rectangles of 3x6

Now let's look at the top and bottom faces, we see that their dimensions are 5 and 6,

Therefore, there are two more rectangles that are size 5x6

That is, there are
2 rectangles 5X6

2 rectangles 3X5

2 rectangles 6X3

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.

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.

Let's find the surface area of the cuboid step by step:

First, we determine the side length of the square base. Since the area of the square base is given as $25 \, \text{cm}^2$, we have:

Now, using the surface area formula for a cuboid with a square base:

Substitute the values $s = 5 \, \text{cm}$ and $h = 3 \, \text{cm}$:

Therefore, the surface area of the cuboid is 110 cm².

To solve this problem, we will use the formula for the surface area of a cuboid:

$S = 2(lw + lh + wh)$

Given:

• Surface area, $S = 102$
• Length, $l = 7$
• Width, $w = 3$
• Height, $h = X$

Substitute the known values into the surface area formula:

$102 = 2(7 \cdot 3 + 7 \cdot X + 3 \cdot X)$

Simplify by calculating the known products:

$102 = 2(21 + 7X + 3X)$

Combine like terms:

$102 = 2(21 + 10X)$

Distribute the 2 across the terms inside the parentheses:

$102 = 42 + 20X$

To isolate $X$, subtract 42 from both sides:

$60 = 20X$

Finally, divide both sides by 20 to solve for $X$:

$X = \frac{60}{20} = 3$

Therefore, the solution to the problem is $X = 3$.

To solve the problem, let's recall the formula for calculating the surface area of a cube:

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

Let's substitute the known values into the formula, labelling the missing side X:

2*(3*7+7*X+3*X) = 122

2*(21+7x+3x) = 122

2(21+10x) = 122

Let's now expand the parentheses:

42+20x=122

Now we move terms:

20x=122-42

20x=80

Finally, simplify:

x=4

And that's the solution!

Given the surface area of a cuboid formula:

$S = 2(lw + lh + wh)$

We have one fixed dimension as 17 cm. However, we do not know which two dimensions among length ($l$), width ($w$), or height ($h$) correspond to this value. Our goal is to solve the expression with this unknown configuration as:

$2(17\cdot w + 17\cdot h + wh) = 147$

Simplifying gives:

$17w + 17h + wh = 73.5$

Further simplification only provides combinations for dimensions.
However, no logical combination allows us to solve this equation since the equation involves three variables but is provided just a single constraint (surface area).

Therefore, identifying the dimensions from the given information is impossible without additional details or constraints on the remaining dimensions.

Given the specified choices, the correct conclusion for the problem is "Impossible to calculate."

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

• Step 1: Convert all dimensions to the same unit.

• Step 2: Apply the surface area formula for a cuboid.

• Step 3: Calculate the total surface area.

Now, let's work through each step:

Step 1: Convert all dimensions to the same unit. For consistency, we will convert everything to decimeters (dm):

• Width = 5 dm (already in dm)

• Height = 4 cm. To convert cm to dm, divide by 10: $4 \, \text{cm} = 0.4 \, \text{dm}$.

• Depth = 0.3 dm (already in dm)

Step 2: Apply the surface area formula for a cuboid:

The surface area $A$ is given by:

$A = 2lw + 2lh + 2wh$

Where:

• $l = 0.3 \, \text{dm}$ (depth)

• $w = 5 \, \text{dm}$ (width)

• $h = 0.4 \, \text{dm}$ (height converted to dm)

Substitute these values into the formula:

$A = 2(0.3)(5) + 2(0.3)(0.4) + 2(5)(0.4)$

Step 3: Calculate the surface area:

$A = 2(1.5) + 2(0.12) + 2(2)$

$A = 3 + 0.24 + 4$

$A = 7.24 \, \text{dm}^2$

Note that the question requires the surface area in different units.

Thus, 7.24 dm² is 72.4 cm²

Therefore, the solution to the problem is 72.4 cm².

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

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for the surface area of a cube.
• Step 3: Solve the equation to find the side length.

Now, let's work through each step:

Step 1: The problem gives us that the surface area of the cube is 24 cm².

Step 2: We'll use the formula for the surface area of a cube: $A = 6s^2$, where $A$ is the surface area and $s$ is the side length.

Step 3: Substitute the given surface area into the formula and solve for $s$:

$6s^2 = 24$

Divide both sides by 6 to isolate $s^2$:

$s^2 = \frac{24}{6} = 4$

Take the square root of both sides to solve for $s$:

$s = \sqrt{4} = 2$

Therefore, the solution to the problem is $s = 2$ cm.

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