**Find the Length of the Missing Side of a Prism**To find the length of the missing side of a given prism, follow the instructions below. We have the dimensions of the other two sides and the volume of the prism.**Given Dimensions:**- One side: 4 cm- Second side: 5 cm- Third side: $ y $ cm (unknown, to be found)- Volume of the prism: $ 160 \, \text{cm}^3 $**Formula for the volume of a rectangular prism:**\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]Here, the volume of the prism is given, and we need to find the missing side $ y $.**Calculation Steps:**1. Substitute the known values into the volume formula:\[ 160 \, \text{cm}^3 = 4 \, \text{cm} \times 5 \, \text{cm} \times y \, \text{cm} \]2. Simplify the equation:\[ 160 = 20 \times y \]3. Solve for $ y $ by dividing both sides by 20:\[ y = \frac{160}{20} \]\[ y = 8 \, \text{cm} \]**Correct Answer:**\[ y = 8 \, \text{cm} \]### Explanation of Graph/Diagram:The diagram represents a rectangular prism (3D box) with the following labels in the given image:- The length of one side is labeled as 4 cm.- The length of another side is labeled as 5 cm.- The length of the third side is labeled as $ y $ cm, which is unknown.- The total volume of the prism is stated to be 160 cubic centimeters.**Multiple Choice Options:** - $ \bigcirc \, 2 \, \text{cm} $- $ \bigcirc \, 4 \, \text{cm} $- $ \bigcirc \, 5 \, \text{cm} $- $ \bigcirc \, 6 \, \text{cm} $- $ \bigcirc \, 8 \, \text{cm} $ (highlighted indicating it's the chosen answer)The correct

The box has dimensions 4cm, 5cm, y cm and volume 160 cubic cm.

Answered: Find the length of the missing side y…

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Geometry

Find the length of the missing side y cm 4 cm 5 cm If the volume of prism is 160 cm3, y =

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter6: Quadratic Equations And Inequalities

Section6.5: More Quadratic Equations And Applications

Problem 52PS: A 5-inch by 7-inch picture is surrounded by a frame of uniform width. The area of the picture and...

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**Find the Length of the Missing Side of a Prism**

To find the length of the missing side of a given prism, follow the instructions below. We have the dimensions of the other two sides and the volume of the prism.

**Given Dimensions:**
- One side: 4 cm
- Second side: 5 cm
- Third side: $ y $ cm (unknown, to be found)
- Volume of the prism: $ 160 \, \text{cm}^3 $

**Formula for the volume of a rectangular prism:**
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

Here, the volume of the prism is given, and we need to find the missing side $ y $.

**Calculation Steps:**
1. Substitute the known values into the volume formula:
\[ 160 \, \text{cm}^3 = 4 \, \text{cm} \times 5 \, \text{cm} \times y \, \text{cm} \]
2. Simplify the equation:
\[ 160 = 20 \times y \]
3. Solve for $ y $ by dividing both sides by 20:
\[ y = \frac{160}{20} \]
\[ y = 8 \, \text{cm} \]

**Correct Answer:**
\[ y = 8 \, \text{cm} \]

### Explanation of Graph/Diagram:
The diagram represents a rectangular prism (3D box) with the following labels in the given image:
- The length of one side is labeled as 4 cm.
- The length of another side is labeled as 5 cm.
- The length of the third side is labeled as $ y $ cm, which is unknown.
- The total volume of the prism is stated to be 160 cubic centimeters.

**Multiple Choice Options:**
- $ \bigcirc \, 2 \, \text{cm} $
- $ \bigcirc \, 4 \, \text{cm} $
- $ \bigcirc \, 5 \, \text{cm} $
- $ \bigcirc \, 6 \, \text{cm} $
- $ \bigcirc \, 8 \, \text{cm} $ (highlighted indicating it's the chosen answer)

The correct

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