Find the Length EG in a Cuboid with Volume 70 cm³

Q: Why do we multiply the three dimensions for volume?

Volume measures 3D space! Think of it as layers: if you have a 2×5 rectangle, that's the area of one layer. Stack 7 of these layers and you get 2 × 5 × 7 = 70 unit cubes total.

Q: How do I identify which dimension is which in the diagram?

Look for the labeled measurements on the edges. In this cuboid, you can see '5' on one edge and '7' on the bottom. The unmarked edge EG is what we need to find.

Q: What if I get the wrong answer when I substitute back?

Double-check your arithmetic! Make sure you divided correctly: $ \frac{70}{35} = 2 $. If your calculation gives a different result, review each step carefully.

Q: Can volume ever be negative?

Never! Volume represents physical space, so it's always positive. If you get a negative answer, check your calculation - you likely made an error somewhere.

Q: What units should my answer have?

Since we're finding a length (side EG), the answer should be in length units - in this case cm. Volume has cubic units (cm³), but individual dimensions have linear units (cm).

Volume Formula with Missing Dimension

The volume of a cuboid is 70 cm³.

Work out the length of the side EG.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find EG

00:04 We'll use the formula for calculating box volume

00:08 height times length times width

00:12 We'll substitute appropriate values and solve for EG

00:33 Isolate EG

00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The volume of a cuboid is 70 cm³.

Work out the length of the side EG.

Step-by-step solution

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.

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For cuboids, Volume = length × width × height
Technique: Rearrange to find missing dimension: $l = \frac{V}{w \times h} = \frac{70}{5 \times 7} = 2$
Check: Verify by multiplying back: 2 × 5 × 7 = 70 cm³ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add the dimensions like 2 + 5 + 7 = 14 cm³! Volume measures 3D space by multiplying all three dimensions together. Always use V = l × w × h for cuboids.

Practice Quiz

Test your knowledge with interactive questions

Calculate the volume of the rectangular prism below using the data provided.

FAQ

Everything you need to know about this question

Why do we multiply the three dimensions for volume?

Volume measures 3D space! Think of it as layers: if you have a 2×5 rectangle, that's the area of one layer. Stack 7 of these layers and you get 2 × 5 × 7 = 70 unit cubes total.

How do I identify which dimension is which in the diagram?

Look for the labeled measurements on the edges. In this cuboid, you can see '5' on one edge and '7' on the bottom. The unmarked edge EG is what we need to find.

What if I get the wrong answer when I substitute back?

Double-check your arithmetic! Make sure you divided correctly: $\frac{70}{35} = 2$ . If your calculation gives a different result, review each step carefully.

Can volume ever be negative?

Never! Volume represents physical space, so it's always positive. If you get a negative answer, check your calculation - you likely made an error somewhere.

What units should my answer have?

Since we're finding a length (side EG), the answer should be in length units - in this case cm. Volume has cubic units (cm³), but individual dimensions have linear units (cm).

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