Surface Area of a Cuboid: Applying the formula

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 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'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 calculate the surface area of the rectangular prism, we will need to identify its three faces (each face appears twice):

1*3

1*8

3*8

The formula for the surface area of a rectangular prism is the sum of all the areas of the faces, that is:

We replace the data in the formula:

2*(1*3+1*8+3*8)=
2*(3+8+24) = 
2*35 = 

70

And this is the solution!

To solve this problem, we will calculate the volume and surface area of a cube with edge length 8 cm.

• Step 1: Calculate the volume of the cube using the formula $V = a^3$.

Given that the edge length $a = 8$ cm, the volume is calculated as follows:

$V = 8^3 = 8 \times 8 \times 8 = 512 \text{ cm}^3$

• Step 2: Calculate the surface area of the cube using the formula $S = 6a^2$.

Using the same edge length $a = 8$ cm, we find the surface area:

$S = 6 \times 8^2 = 6 \times (8 \times 8) = 6 \times 64 = 384 \text{ cm}^2$

Thus, the calculated volume and surface area of the cube are, respectively, 512 cm$^3$ and 384 cm$^2$.

Therefore, the correct solution to the problem, matching the given answer choices, is choice 1: $V = 512, S = 384$.