Math / Geometry

QuestionNote: Figure is not drawn to scale.
If $a=2.3$ units, $b=4$ units, $c=6$ units, and $d=8$ units, what is the volume of the two prisms? A. 159.74 cubic units B. 256 cubic units C. 127.74 cubic units D. 105.34 cubic units

Studdy Solution

STEP 1

What is this asking? We need to find the total volume of two rectangular prisms stacked together, given their dimensions. Watch out! Don't forget to add the volumes of both prisms!

STEP 2

1. Calculate the volume of the bottom prism.
2. Calculate the volume of the top prism.
3. Calculate the total volume.

STEP 3

The bottom prism has dimensions $a \times a \times c$ .
Remember, the volume of a rectangular prism is length times width times height!

STEP 4

We are given $a = \textbf{2.3}$ units and $c = \textbf{6}$ units.
Let's plug these values into the volume formula: $\text{Volume}_{\text{bottom}} = a \cdot a \cdot c = 2.3 \cdot 2.3 \cdot 6$

STEP 5

Time to calculate!
First, $2.3 \cdot 2.3 = 5.29$ .
Then, $5.29 \cdot 6 = \textbf{31.74}$ .
So, the volume of the bottom prism is $\textbf{31.74}$ cubic units.
Awesome!

STEP 6

The top prism has dimensions $a \times b \times d$ .
We'll use the same volume formula: length times width times height.

STEP 7

We know $a = \textbf{2.3}$ units, $b = \textbf{4}$ units, and $d = \textbf{8}$ units.
Substituting these values into the formula gives us: $\text{Volume}_{\text{top}} = a \cdot b \cdot d = 2.3 \cdot 4 \cdot 8$

STEP 8

Let's multiply! $2.3 \cdot 4 = 9.2$ .
Then, $9.2 \cdot 8 = \textbf{73.6}$ .
Therefore, the volume of the top prism is $\textbf{73.6}$ cubic units.
Fantastic!

STEP 9

To find the total volume, we just need to add the volumes of the two prisms together.
We found that the bottom prism has a volume of $\textbf{31.74}$ cubic units, and the top prism has a volume of $\textbf{73.6}$ cubic units.

STEP 10

Adding these together: $\text{Total Volume} = \text{Volume}_{\text{bottom}} + \text{Volume}_{\text{top}} = 31.74 + 73.6$

STEP 11

$31.74 + 73.6 = \textbf{105.34}$ cubic units.
This is our final answer!

STEP 12

The total volume of the two prisms is $\textbf{105.34}$ cubic units, which corresponds to answer choice D.

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QuestionNote: Figure is not drawn to scale.
If $a=2.3$ units, $b=4$ units, $c=6$ units, and $d=8$ units, what is the volume of the two prisms? A. 159.74 cubic units B. 256 cubic units C. 127.74 cubic units D. 105.34 cubic units

Studdy Solution

STEP 1

What is this asking? We need to find the total volume of two rectangular prisms stacked together, given their dimensions. Watch out! Don't forget to add the volumes of both prisms!

STEP 2

1. Calculate the volume of the bottom prism.
2. Calculate the volume of the top prism.
3. Calculate the total volume.

STEP 3

The bottom prism has dimensions $a \times a \times c$ .
Remember, the volume of a rectangular prism is length times width times height!

STEP 4

We are given $a = \textbf{2.3}$ units and $c = \textbf{6}$ units.
Let's plug these values into the volume formula: $\text{Volume}_{\text{bottom}} = a \cdot a \cdot c = 2.3 \cdot 2.3 \cdot 6$

STEP 5

Time to calculate!
First, $2.3 \cdot 2.3 = 5.29$ .
Then, $5.29 \cdot 6 = \textbf{31.74}$ .
So, the volume of the bottom prism is $\textbf{31.74}$ cubic units.
Awesome!

STEP 6

The top prism has dimensions $a \times b \times d$ .
We'll use the same volume formula: length times width times height.

STEP 7

We know $a = \textbf{2.3}$ units, $b = \textbf{4}$ units, and $d = \textbf{8}$ units.
Substituting these values into the formula gives us: $\text{Volume}_{\text{top}} = a \cdot b \cdot d = 2.3 \cdot 4 \cdot 8$

STEP 8

Let's multiply! $2.3 \cdot 4 = 9.2$ .
Then, $9.2 \cdot 8 = \textbf{73.6}$ .
Therefore, the volume of the top prism is $\textbf{73.6}$ cubic units.
Fantastic!

STEP 9

To find the total volume, we just need to add the volumes of the two prisms together.
We found that the bottom prism has a volume of $\textbf{31.74}$ cubic units, and the top prism has a volume of $\textbf{73.6}$ cubic units.

STEP 10

Adding these together: $\text{Total Volume} = \text{Volume}_{\text{bottom}} + \text{Volume}_{\text{top}} = 31.74 + 73.6$

STEP 11

$31.74 + 73.6 = \textbf{105.34}$ cubic units.
This is our final answer!

STEP 12

The total volume of the two prisms is $\textbf{105.34}$ cubic units, which corresponds to answer choice D.

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QuestionNote: Figure is not drawn to scale.If a=2.3a=2.3a=2.3 units, b=4b=4b=4 units, c=6c=6c=6 units, and d=8d=8d=8 units, what is the volume of the two prisms? A. 159.74 cubic units B. 256 cubic units C. 127.74 cubic units D. 105.34 cubic units

Studdy Solution

STEP 1

What is this asking? We need to find the total volume of two rectangular prisms stacked together, given their dimensions. Watch out! Don't forget to add the volumes of *both* prisms!

STEP 2

1. Calculate the volume of the bottom prism.2. Calculate the volume of the top prism.3. Calculate the total volume.

STEP 3

The bottom prism has dimensions a×a×ca \times a \times ca×a×c.Remember, the **volume** of a rectangular prism is length times width times height!

STEP 4

We are given a=2.3a = \textbf{2.3}a=2.3 units and c=6c = \textbf{6}c=6 units.Let's plug these values into the volume formula: Volumebottom=a⋅a⋅c=2.3⋅2.3⋅6 \text{Volume}_{\text{bottom}} = a \cdot a \cdot c = 2.3 \cdot 2.3 \cdot 6 Volumebottom​=a⋅a⋅c=2.3⋅2.3⋅6

STEP 5

Time to **calculate**!First, 2.3⋅2.3=5.292.3 \cdot 2.3 = 5.292.3⋅2.3=5.29.Then, 5.29⋅6=31.745.29 \cdot 6 = \textbf{31.74}5.29⋅6=31.74.So, the volume of the bottom prism is 31.74\textbf{31.74}31.74 cubic units.Awesome!

STEP 6

The top prism has dimensions a×b×da \times b \times da×b×d.We'll use the same **volume formula**: length times width times height.

STEP 7

We know a=2.3a = \textbf{2.3}a=2.3 units, b=4b = \textbf{4}b=4 units, and d=8d = \textbf{8}d=8 units.Substituting these values into the formula gives us: Volumetop=a⋅b⋅d=2.3⋅4⋅8 \text{Volume}_{\text{top}} = a \cdot b \cdot d = 2.3 \cdot 4 \cdot 8 Volumetop​=a⋅b⋅d=2.3⋅4⋅8

STEP 8

Let's **multiply**! 2.3⋅4=9.22.3 \cdot 4 = 9.22.3⋅4=9.2.Then, 9.2⋅8=73.69.2 \cdot 8 = \textbf{73.6}9.2⋅8=73.6.Therefore, the volume of the top prism is 73.6\textbf{73.6}73.6 cubic units.Fantastic!

STEP 9

To find the **total volume**, we just need to add the volumes of the two prisms together.We found that the bottom prism has a volume of 31.74\textbf{31.74}31.74 cubic units, and the top prism has a volume of 73.6\textbf{73.6}73.6 cubic units.

STEP 10

Adding these together: Total Volume=Volumebottom+Volumetop=31.74+73.6 \text{Total Volume} = \text{Volume}_{\text{bottom}} + \text{Volume}_{\text{top}} = 31.74 + 73.6 Total Volume=Volumebottom​+Volumetop​=31.74+73.6

STEP 11

31.74+73.6=105.3431.74 + 73.6 = \textbf{105.34}31.74+73.6=105.34 cubic units.This is our **final answer**!

STEP 12

The total volume of the two prisms is 105.34\textbf{105.34}105.34 cubic units, which corresponds to answer choice D.

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QuestionNote: Figure is not drawn to scale.
If $a=2.3$ units, $b=4$ units, $c=6$ units, and $d=8$ units, what is the volume of the two prisms? A. 159.74 cubic units B. 256 cubic units C. 127.74 cubic units D. 105.34 cubic units

What is this asking? We need to find the total volume of two rectangular prisms stacked together, given their dimensions. Watch out! Don't forget to add the volumes of both prisms!

1. Calculate the volume of the bottom prism.
2. Calculate the volume of the top prism.
3. Calculate the total volume.

The bottom prism has dimensions $a \times a \times c$ .
Remember, the volume of a rectangular prism is length times width times height!

We are given $a = \textbf{2.3}$ units and $c = \textbf{6}$ units.
Let's plug these values into the volume formula: $\text{Volume}_{\text{bottom}} = a \cdot a \cdot c = 2.3 \cdot 2.3 \cdot 6$

Time to calculate!
First, $2.3 \cdot 2.3 = 5.29$ .
Then, $5.29 \cdot 6 = \textbf{31.74}$ .
So, the volume of the bottom prism is $\textbf{31.74}$ cubic units.
Awesome!

The top prism has dimensions $a \times b \times d$ .
We'll use the same volume formula: length times width times height.

We know $a = \textbf{2.3}$ units, $b = \textbf{4}$ units, and $d = \textbf{8}$ units.
Substituting these values into the formula gives us: $\text{Volume}_{\text{top}} = a \cdot b \cdot d = 2.3 \cdot 4 \cdot 8$

Let's multiply! $2.3 \cdot 4 = 9.2$ .
Then, $9.2 \cdot 8 = \textbf{73.6}$ .
Therefore, the volume of the top prism is $\textbf{73.6}$ cubic units.
Fantastic!

To find the total volume, we just need to add the volumes of the two prisms together.
We found that the bottom prism has a volume of $\textbf{31.74}$ cubic units, and the top prism has a volume of $\textbf{73.6}$ cubic units.

Adding these together: $\text{Total Volume} = \text{Volume}_{\text{bottom}} + \text{Volume}_{\text{top}} = 31.74 + 73.6$

$31.74 + 73.6 = \textbf{105.34}$ cubic units.
This is our final answer!

The total volume of the two prisms is $\textbf{105.34}$ cubic units, which corresponds to answer choice D.