Calculate Rectangular Prism Volume Using Areas of 15 cm² and 24 cm²

Q: How do I know which edge belongs to which rectangle?

Look at the vertex labels carefully! Rectangle CAEG shares edge AE with rectangle ABFE. The edge AE = 3 is common to both rectangles, so use it to find the other dimensions.

Q: Why can't I just multiply the two given areas together?

Areas are 2-dimensional measurements, not the 3D dimensions you need for volume! You must use Area = length × width to find each missing dimension first.

Q: What if I can't see the 3D shape clearly in the diagram?

Focus on the rectangle names instead! CAEG and ABFE tell you exactly which vertices form each rectangle. The shared letters (A and E) show the common edge.

Q: How do I check if my volume answer is reasonable?

Compare your dimensions: 3 cm × 5 cm × 8 cm. The volume 120 cm³ should be larger than any single face area (15 cm² or 24 cm²), which makes sense!

Volume Calculation with Given Face Areas

Look at the rectangular prism below.

The area of rectangle CAEG is 15 cm².

The area of rectangle ABFE is 24 cm².

Calculate the volume of the rectangular prism ABCDEFGH.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the volume of box ABCDEFGH

00:03 Data values

00:10 Mark side GE with letter X

00:13 Use the formula to calculate rectangle area length times width

00:16 Insert appropriate values and solve for X

00:20 This is the length GE

00:23 Now use the same method to find EF

00:29 Mark EF with letter Y

00:33 Insert into formula for rectangle area and solve for Y

00:38 This is the width EF

00:41 Calculate volume using length(8) times width(5) times height(3)

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

Look at the rectangular prism below.

The area of rectangle CAEG is 15 cm².

The area of rectangle ABFE is 24 cm².

Calculate the volume of the rectangular prism ABCDEFGH.

Step-by-step solution

Since we are given the area of rectangle CAEG and length AE, we can find GE:

Let's denote GE as X and substitute the data in the rectangle area formula:

$3\times x=15$

Let's divide both sides by 3:

$x=5$

Therefore GE equals 5

Since we are given the area of rectangle ABFE and length AE, we can find EF:

Let's denote EF as Y and substitute the data in the rectangle area formula:

$3\times y=24$

Let's divide both sides by 3:

$y=8$

Therefore EF equals 8

Now we can calculate the volume of the box:

$3\times5\times8=15\times8=120$

Final Answer

$120$

Key Points to Remember

Essential concepts to master this topic

Rectangular Prism Dimensions: Use given face areas and shared edges to find all three dimensions
Finding Unknown Dimensions: From Area = length × width, solve $15 = 3 \times x$ to get x = 5
Volume Verification: Check that $3 \times 5 \times 8 = 120$ cm³ using all three dimensions ✓

Common Mistakes

Avoid these frequent errors

Using area values directly as volume without finding dimensions
Don't multiply the given areas (15 × 24 = 360) thinking this gives volume! This ignores the rectangular prism structure and shared edges. Always find the three individual dimensions first using Area = length × width, then multiply length × width × height for volume.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

How do I know which edge belongs to which rectangle?

Look at the vertex labels carefully! Rectangle CAEG shares edge AE with rectangle ABFE. The edge AE = 3 is common to both rectangles, so use it to find the other dimensions.

Why can't I just multiply the two given areas together?

Areas are 2-dimensional measurements, not the 3D dimensions you need for volume! You must use Area = length × width to find each missing dimension first.

What if I can't see the 3D shape clearly in the diagram?

Focus on the rectangle names instead! CAEG and ABFE tell you exactly which vertices form each rectangle. The shared letters (A and E) show the common edge.

How do I check if my volume answer is reasonable?

Compare your dimensions: 3 cm × 5 cm × 8 cm. The volume 120 cm³ should be larger than any single face area (15 cm² or 24 cm²), which makes sense!

What if I get the dimensions mixed up?

It doesn't matter which dimension you call length, width, or height! As long as you multiply all three dimensions together, you'll get the correct volume of 120 cm³.

🌟 Unlock Your Math Potential

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

Calculate Rectangular Prism Volume Using Areas of 15 cm² and 24 cm²

Volume Calculation with Given Face Areas

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which edge belongs to which rectangle?

Why can't I just multiply the two given areas together?

What if I can't see the 3D shape clearly in the diagram?

How do I check if my volume answer is reasonable?

What if I get the dimensions mixed up?

🌟 Unlock Your Math Potential

More Questions

Volume of a Orthohedron

Calculate the Volume of a Cuboid: Step-by-Step Measurement Guide

Calculate Building Volume: Find Expression for 21×15×(14+30X) Meters³

Calculate Cuboid Volume: Finding Volume in Terms of X with Dimensions (5+X, 4+X, 7)

Find Side Length HF in a Cuboid with Volume 60 cm³

Area of a Rectangle

Calculate Rectangle Area: Using Distributive Property with (4+5) × 7

Calculate Rectangle Area: Using Distributive Property with (9+4)(3+2)

Calculate Cuboid Volume: Rectangle Base 12 cm² with Height 3

Calculate Cuboid Volume: Using Rectangle Area of 20 cm²