Cuboids Practice Problems & Three-Dimensional Figures

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

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

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 determine the volume of a cuboid, we apply the formula:

• Step 1: Identify the dimensions of the cuboid:
  • Length ($l$) = 12 cm
  • Width ($w$) = 8 cm
  • Height ($h$) = 5 cm
• Step 2: Apply the volume formula for a cuboid:

The formula to find the volume ($V$) of a cuboid is:

$V = l \times w \times h$

Step 3: Substitute the given dimensions into the formula and calculate: $V = 12 \times 8 \times 5$

Step 4: Perform the multiplication in stages for clarity:

First, calculate $12 \times 8 = 96$

Then multiply the result by 5: $96 \times 5 = 480$

Therefore, the volume of the cuboid is $\mathbf{480 \, \text{cm}^3}$.

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

• Step 1: Identify the dimensions of each pair of rectangles given the orthohedron's dimensions.
• Step 2: Each face of a cuboid corresponds to a rectangle, with three distinct pairs of dimensions.
• Step 3: Identify all pairs of dimensions and count the pairs that form sets of rectangles.

Now, let's work through each step:
Step 1: The orthohedron's dimensions are given as $4$, $7$, and $10$.
Step 2: A cuboid (orthohedron) has three pairs of opposite rectangular faces:
- Pair 1: Two rectangles with dimensions $4 \times 7$.
- Pair 2: Two rectangles with dimensions $4 \times 10$.
- Pair 3: Two rectangles with dimensions $7 \times 10$.
Step 3: Count each of the pairs to verify the total number of rectangles formed.
We find there are 6 rectangles in total, with the dimensions specified above fulfilling the conditions for each face of the cuboid.

The solution to the problem is that the orthohedron is formed of:
2 Rectangles $4 \times 7$,
2 Rectangles $4 \times 10$,
2 Rectangles $7 \times 10$.

These dimensions and quantities match choice #3 in the answer options provided.