Volume of a Orthohedron: Calculation using percentages

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

• Step 1: Determine the length of the cuboid as a percentage of the width.
• Step 2: Calculate the height of the cuboid as a percentage increase from the length.
• Step 3: Use the dimensions to calculate the volume of the cuboid.

Now, let's work through each step:

Step 1: Calculate the length:

$L = W \times (1 - 0.40) = 10 \, \text{cm} \times 0.60 = 6 \, \text{cm}$

Step 2: Calculate the height:

$H = L \times 1.50 = 6 \, \text{cm} \times 1.50 = 9 \, \text{cm}$

Step 3: Calculate the volume:

$V = W \times L \times H = 10 \, \text{cm} \times 6 \, \text{cm} \times 9 \, \text{cm} = 540 \, \text{cm}^3$

Therefore, the volume of the cuboid is $\mathbf{540 \, \text{cm}^3}$.

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

• Step 1: Calculate the dimensions of the prism using the given percentages.
• Step 2: Apply the volume formula for a rectangular prism.
• Step 3: Perform the necessary calculations to find the volume.

Now, let's work through each step:
Step 1: Given the width $W = 12 \, \text{cm}$.
- Length $L = 0.4 \times W = 0.4 \times 12 = 4.8 \, \text{cm}$.
- Height $H = 0.3 \times W = 0.3 \times 12 = 3.6 \, \text{cm}$.

Step 2: Use the volume formula: $V = L \times W \times H$.

Step 3: Substitute the values:
$V = 4.8 \times 12 \times 3.6$.
Calculate $V = 207.36 \, \text{cm}^3$.

Therefore, the volume of the rectangular prism is approximately $207.36 \, \text{cm}^3$.
The answer closest to this value, accounting for rounding to match choices given, is 207.3 cm³.

The correct answer is choice 2: 207.3 cm³.

To solve this problem, we'll calculate the volume of the cube directly given its edge length:

• Step 1: Recall that the volume $V$ of a cube with edge length $a$ is given by the formula $V = a^3$.
• Step 2: We are provided the edge length $a = 9$ cm.
• Step 3: Substitute $a = 9$ cm into the formula for the volume: $V = 9^3$.
• Step 4: Calculate $9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729$ cm³.

However, this reveals a discrepancy, as the originally provided answer should have been revisited. The initial error here appears to be with not correcting the originally context-provided solution. In the typical context, the answer would indeed be 729 cm³, not the 243 cm³ which is inconsistent with proper cube volume calculations.

Thus, the correct calculation is that the volume of the cube is indeed $729 \, \text{cm}^3$, matching the accurate interpretation of the inputs.

To solve this problem of finding the volume of the given cuboid, we will follow these detailed steps:

First, we need to calculate the length of the cuboid:

• The width is given as $10 \, \text{cm}$.
• The length is $40\%$ smaller than the width, so we calculate the change as $0.40 \times 10 \, \text{cm} = 4 \, \text{cm}$.
• Thus, the length is $10 \, \text{cm} - 4 \, \text{cm} = 6 \, \text{cm}$.

Next, we calculate the height of the cuboid:

• The height is $50\%$ of the length.
• Thus, the height is $0.50 \times 6 \, \text{cm} = 3 \, \text{cm}$.

Finally, calculate the volume of the cuboid using the formula:

• The volume $V$ is given by $V = \text{length} \times \text{width} \times \text{height}$.
• Substitute the known values: $V = 6 \, \text{cm} \times 10 \, \text{cm} \times 3 \, \text{cm}$.
• Perform the multiplication: $V = 180 \, \text{cm}^3$.

Therefore, the volume of the cuboid is $180 \, \text{cm}^3$.

To solve this problem, we must calculate the missing dimensions of the cuboid and use the volume formula:

• Step 1: Determine the length of the cuboid.
• Step 2: Calculate the height of the cuboid.
• Step 3: Compute the volume using the cuboid's dimensions.

Let's work through each step in detail:

Step 1: Determine the Length.

The width of the cuboid is given as $10 \, \text{cm}$. The length is 40% less than the width. To find the length:

$\text{Length} = \text{Width} - 0.4 \times \text{Width}$

$\text{Length} = 10 - 0.4 \times 10 = 10 - 4 = 6 \, \text{cm}$

Step 2: Calculate the Height.

The height is 50% greater than the length. To find the height:

$\text{Height} = \text{Length} + 0.5 \times \text{Length}$

$\text{Height} = 6 + 0.5 \times 6 = 6 + 3 = 9 \, \text{cm}$

Step 3: Compute the Volume.

The volume of the cuboid is given by:

$V = \text{Length} \times \text{Width} \times \text{Height}$

$V = 6 \times 10 \times 9 = 540 \, \text{cm}^3$

Thus, the volume of the cuboid is $\boxed{540 \, \text{cm}^3}$.

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

• Step 1: Identify the given information and calculate the length and height.

• Step 2: Apply the formula for the volume of a cuboid.

• Step 3: Perform the necessary calculations to find the volume.

Now, let's work through each step:

Step 1: Identify the given information and calculate the dimensions

We know the cuboid has a width of $w = 12$ cm. The length $l$ is stated to be 40% of this width. Thus, we calculate:
$l = 0.4 \times 12 = 4.8$ cm.

The height $h$ is 30% of the width, so:
$h = 0.3 \times 12 = 3.6$ cm.

Step 2: Apply the formula for the volume of a cuboid

The formula for the volume of a cuboid is given by $V = l \times w \times h$.

Step 3: Calculate the volume

Now, substitute the values for $l$, $w$, and $h$:
$V = 4.8 \times 12 \times 3.6 = 207.36$ cm³.

Therefore, the volume of the cuboid is $207.36$ cm³.