Volume of a Orthohedron: Calculate The Missing Side based on the formula

The formula for the volume of a box is height*length*width

In the specific question, we are given the volume and the height,

and we are looking for the area of the base,

As you will remember, the area is length * width

If we replace all the data in the formula, we see that:

4 * the area of the base = 80

Therefore, if we divide by 4 we see that

Area of the base = 20

To find the value of $X$, we begin by using the formula for the volume of a cuboid, which is given by $V = \text{height} \times \text{depth} \times \text{width}$.

In this problem, the volume $V$ is 90 cubic units, the height is 5 units, and the depth is 3 units. We need to find the width $X$. So, we write the equation:

Simplify the equation:

To solve for $X$, divide both sides of the equation by 15:

Calculating the right-hand side, we find:

Thus, the width of the cuboid, $X$, is 6 units.

The correct answer to the multiple-choice question is choice 4: 6.

Volume formula for a rectangular prism:

Volume = length X width X height

Therefore, first we will place the data we are given into the formula:

45 = 2.5*4*X

We divide both sides of the equation by 2.5:

18=4*X

And now we divide both sides of the equation by 4:

4.5 = X

To find the width of the rectangular prism, we'll start by using the formula for the volume of a rectangular prism:

$V = \text{length} \times \text{width} \times \text{height}$

We are given that the volume $V = 880 \, \text{cm}^3$, the length $\text{length} = 8 \, \text{cm}$, and the height $\text{height} = 10 \, \text{cm}$. We need to find the width, which we'll denote as $w$.

Substitute the known values into the formula:

$880 = 8 \times w \times 10$

Simplify the equation:

$880 = 80 \times w$

To solve for $w$, divide both sides of the equation by 80:

$w = \frac{880}{80}$

Simplify the fraction:

$w = 11$

Therefore, the width of the rectangular prism is $\textbf{11 cm}$.

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

• Step 1: Apply the formula for the volume of a cuboid: $V = l \times w \times h$.
• Step 2: Substitute the known values: $924 = 12 \times 7 \times X$.
• Step 3: Simplify and solve for $X$.

Now, let's work through each step:
Step 1: The formula for the volume of the cuboid is $V = l \times w \times h$.
Step 2: Substitute the given values into the formula: $924 = 12 \times 7 \times X$.
Step 3: Calculate $12 \times 7$ which equals 84. Thus, $924 = 84 \times X$.
Step 4: Solve for $X$ by dividing both sides by 84:
$\frac{924}{84} = X$
Perform the division: $924 \div 84 = 11$.

Therefore, the value of $X$ is $11$.

To solve this problem, follow these steps:

• Step 1: Identify the known values and the formula.
• Step 2: Substitute the known values into the formula and solve for the unknown.
• Step 3: Perform the calculations to find the height.

Now, let's work through each step:

Step 1: We know the length ($L$) is $8 \, \text{cm}$, the width ($W$) is $4 \, \text{cm}$, and the volume ($V$) is $96 \, \text{cm}^3$. The formula for the volume of a cuboid is:

$V = L \times W \times H$, where $H$ is the height.

Step 2: Rearrange the formula to solve for $H$:

$H = \frac{V}{L \times W}$

Step 3: Substitute the known values:

$H = \frac{96}{8 \times 4}$

Calculate the denominator:

$8 \times 4 = 32$

Substitute back into the equation:

$H = \frac{96}{32}$

Calculate the height:

$H = 3 \, \text{cm}$.

Therefore, the height of the cuboid is $3 \, \text{cm}$.

To solve this problem, we will first use the formula for the volume of a cuboid:

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

Given:

• Length = $7 \, \text{cm}$
• Height = $4 \, \text{cm}$
• Volume = $84 \, \text{cm}^3$

We need to find the width. We can rearrange the formula to solve for the width:

$\text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}}$

Substitute the given values into the formula:

$\text{Width} = \frac{84}{7 \times 4}$

Calculate the denominator first:

$7 \times 4 = 28$

Now substitute back into the calculation for width:

$\text{Width} = \frac{84}{28}$

Simplify the calculation:

$\text{Width} = 3 \, \text{cm}$

Therefore, the width of the cuboid is $3 \, \text{cm}$.

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us:
- Length ($L$) = $5 \, \text{cm}$
- Width ($W$) = $3 \, \text{cm}$
- Volume ($V$) = $30 \, \text{cm}^3$

Step 2: We'll use the formula:

$V = L \times W \times H$

Step 3: Plug in the known values:

$30 = 5 \times 3 \times H$

Simplify the equation:

$30 = 15 \times H$

To solve for $H$, divide both sides by 15:

$H = \frac{30}{15} = 2 \, \text{cm}$

Therefore, the height of the cuboid is $2 \, \text{cm}$.

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

• Step 1: Identify the given information.
• Step 2: Apply the volume formula for a cuboid.
• Step 3: Rearrange the formula to solve for the unknown dimension.
• Step 4: Perform the necessary calculations.

Let's proceed with each step:

Step 1: The problem provides us with a cuboid with:

• Volume $V = 70$ cm$^3$
• Width $w = 5$ cm
• Height $h = 7$ cm
• The unknown length `l` is side EG.

Step 2: The volume of a cuboid is calculated using the formula:

$V = l \times w \times h$

Step 3: We need to rearrange the formula to solve for the length $l$:

$l = \frac{V}{w \times h}$

Step 4: Substitute the values into the formula:

$l = \frac{70}{5 \times 7}$

$l = \frac{70}{35}$

$l = 2$ cm

Therefore, the length of side EG is $2$ cm and the correct choice is option 3.

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate volume formula
• Step 3: Perform the necessary calculations

Let's work through each step:
Step 1: We know that the area of the base $S$ is 15 m², and the height $h$ is 3 m.
Step 2: We'll use the formula for the volume of a rectangular prism: $V = S \times h$.
Step 3: Plugging in the values, we have $V = 15 \times 3$.

Calculating this gives us $V = 45$ m³.

Therefore, the volume of the rectangular prism is $45 \, \text{m}^3$.

To find the length of the side of the square base, we'll apply the formula for the volume of a cuboid:

$V = l^2 \times h$

Step 1: Substitute the given values into the equation.

We have:

$640 = l^2 \times 10$

Step 2: Simplify the equation.

Divide both sides by 10:

$64 = l^2$

Step 3: Solve for $l$.

Take the square root of both sides:

$l = \sqrt{64}$

$l = 8$

Thus, the length of the side of the base of the cuboid is $8$ cm.

To solve the problem of finding the height of the cuboid, we will follow these steps:

• Step 1: Calculate the area of the square base of the cuboid.
• Step 2: Use the volume formula to set up an equation and solve for the height.

Now, let's work through each step:

Step 1: Calculate the square base area.
The side length of the square base is $s = 10$ cm. Thus, the area of the base is given by:

$\text{Area} = s^2 = 10^2 = 100$ cm$^2$.

Step 2: Use the volume formula.
The volume of the cuboid is given by the formula:

$V = \text{base area} \times h$.

We know the volume $V = 90$ cm$^3$, and the base area is $100$ cm$^2$. Therefore, we have:

$90 = 100 \times h$.

To find the height $h$, solve the equation:

$h = \frac{90}{100} = 0.9$ cm.

Therefore, the solution to the problem is that the height of the cuboid is $0.9$ cm.

To solve this problem, we'll calculate the height $X$ of the rectangular prism using the given volume.

The volume of a rectangular prism is calculated using the formula:

We have the following values:

• Volume ($V$) = $45 \, \text{cm}^3$
• Length = $2.5 \, \text{cm}$
• Width = $4 \, \text{cm}$

Substitute these numbers into the volume formula and solve for $X$:

First, calculate the product of the length and width:

Substitute this back into the equation:

To isolate $X$, divide both sides by 10:

Thus, the height $X$ of the rectangular prism is $4.5 \, \text{cm}$.

To find the missing width ($X$) of the rectangular prism, we start with the volume formula for a rectangular prism:

$V = l \times w \times h$

Here, $l = 3 \, \text{cm}$, $h = 5 \, \text{cm}$, and $V = 90 \, \text{cm}^3$. We need to find $w$ (or $X$).

Substitute the known values into the formula:

$90 = 3 \times X \times 5$

Simplifying, we have:

$90 = 15 \times X$

To solve for $X$, divide both sides of the equation by 15:

$X = \frac{90}{15}$

Calculating this gives:

$X = 6$

Therefore, the calculated width of the rectangular prism is $X = 6 \, \text{cm}$.

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

• Use the volume formula for the rectangular prism: $V = A_{\text{base}} \times h$.
• Rearrange the formula to solve for the base area: $A_{\text{base}} = \frac{V}{h}$.
• Substitute the given values into this rearranged formula.

Now, let's work through these steps:
Step 1: We know the volume $V = 80 \, \text{m}^3$ and the height $h = 4 \, \text{m}$.
Step 2: Using the formula $A_{\text{base}} = \frac{V}{h}$, we substitute the given numbers:
$A_{\text{base}} = \frac{80}{4} \, \text{m}^2$.
Step 3: Perform the division to find the area of the base:
$A_{\text{base}} = 20 \, \text{m}^2$.

Therefore, the area of the base of the rectangular prism is $20 \, \text{m}^2$.

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

• Step 1: Identify the given information.
• Step 2: Apply the rearranged volume formula to solve for the missing dimension.
• Step 3: Perform the necessary calculations to find $X$.

Now, let's work through each step:

Step 1: The problem gives us:

• Volume of the cuboid, $V = 45$
• Width, $w = 4$
• Length, $l = 2.5$

Step 2: We'll use the formula for the volume of a cuboid, rearranged to solve for height $X$:

$X = \frac{V}{l \times w}$

Step 3: Substitute the given values into the formula:

$X = \frac{45}{2.5 \times 4}$

Calculate $2.5 \times 4 = 10$.

Now, divide the volume by this product:

$X = \frac{45}{10} = 4.5$

Therefore, the solution to the problem is $X = 4.5$.

To solve this problem, let's determine the missing dimension $X$ by applying the formula for the volume of a cuboid:

• Step 1: Identify given values: Volume $V = 90$, Height $H = 5$, Length $L = 3$.
• Step 2: Use the volume formula: $V = L \times W \times H$.
• Step 3: Substitute the known values: $90 = 3 \times X \times 5$.
• Step 4: Simplify and solve for $X$. First, calculate $3 \times 5$, which is $15$.
• Step 5: Rearrange the equation: $90 = 15 \times X$.
• Step 6: Solve for $X$ by dividing both sides by 15: $X = \frac{90}{15}$.
• Step 7: Calculate to find $X = 6$.

Thus, the missing width $X$ of the cuboid is $6$.

To solve this problem, we need to find the side length of the cube given that its volume is 1331 cubic units.

We use the formula for the volume of a cube:
$V = a^3$

Here, the volume $V$ is 1331, so substituting into the formula gives:
$1331 = a^3$

To find $a$, take the cube root of both sides:
$a = \sqrt[3]{1331}$

Calculating the cube root, we find:
$a = 11$

Thus, the side length of the cube is $\mathbf{11}$. This corresponds to choice 3 from the options provided.

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

• Step 1: Write out the volume formula $V = x^2 \times h$, where $x$ is the side of the square base and $h$ is the height.
• Step 2: Substitute the given values $V = 36 \, \text{cm}^3$ and $h = 9 \, \text{cm}$ into the formula.
• Step 3: Solve for $x$.

Now, let's work through each step:
Step 1: The volume formula for the prism is $V = x^2 \times h$.
Step 2: Substitute the known values: $36 = x^2 \times 9$.
Step 3: Solve for $x$ by dividing both sides by 9: $x^2 = \frac{36}{9} = 4$.
To find $x$, take the square root of both sides: $x = \sqrt{4} = 2$.

Therefore, the length of each side of the square base is $x = 2 \, \text{cm}$.