A cuboid has a height of 4 cm.
The ratio between its length and its width is 3:2.
The volume of the cuboid is equal to 96 cm³.
Calculate the length of the cuboid.
We have hundreds of course questions with personalized recommendations + Account 100% premium
A cuboid has a height of 4 cm.
The ratio between its length and its width is 3:2.
The volume of the cuboid is equal to 96 cm³.
Calculate the length of the cuboid.
To solve this problem, we need to find the length of the cuboid using its volume and given dimensions. Let's break this down:
Now, simplify and solve for :
Dividing both sides by 24 gives:
Taking the square root of both sides, we find:
Thus, the length of the cuboid is:
Therefore, the solution to the problem is .
6 cm
A rectangular prism has a base measuring 5 units by 8 units.
The height of the prism is 12 units.
Calculate its volume.
The ratio 3:2 tells us the proportion, not the actual measurements! If length was 3 cm and width was 2 cm, the volume would be cm³, not 96 cm³.
When the ratio is 3:2, let length = 3x and width = 2x. The variable x is a scale factor that makes the measurements fit the actual volume.
Since we're dealing with lengths, x must be positive. If you get a negative square root, double-check your equation setup and calculations.
Using variables with ratios is the most reliable method. Guessing and checking might work, but it's time-consuming and you might miss the correct answer.
In this problem, it doesn't matter! Since we multiply length × width, getting 6 cm and 4 cm gives the same volume whether 6 is length or width.
Substitute back: cm³. Also verify the ratio: ✓
Get unlimited access to all 18 Cuboids questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime